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Chemistry Help: Interpret Coefficients As Mole Ratios

Review real example questions for Interpret Coefficients As Mole Ratios in Chemistry.

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Ammonia can be made by the balanced equation $\mathrm{N_2 + 3H_2 \rightarrow 2NH_3}$ According to the coefficients, how many moles of $\mathrm{H_2}$ react with $1$ mol of $\mathrm{N_2}$ ?

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Question 1

Ammonia can be made by the balanced equation $\mathrm{N_2 + 3H_2 \rightarrow 2NH_3}$ According to the coefficients, how many moles of $\mathrm{H_2}$ react with $1$ mol of $\mathrm{N_2}$ ?

$1$ mol
$2$ mol
$3$ mol (correct answer)
$6$ mol

Explanation: This question tests your understanding that coefficients in balanced chemical equations represent mole ratios—the proportional relationships between amounts of reactants consumed and products formed in a chemical reaction. The coefficients in a balanced equation (the numbers in front of chemical formulas) tell you the ratio of MOLES of each substance involved in the reaction: in $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$ , the coefficients 2, 1, and 2 mean that 2 moles of hydrogen gas react with 1 mole of oxygen gas to produce 2 moles of water. This ratio is the fundamental relationship—it means for every 1 mole of O2 consumed, exactly 2 moles of H2 are consumed and exactly 2 moles of H2O are produced. The ratio stays constant no matter how much you scale it: 4 moles H2 with 2 moles O2 makes 4 moles H2O (doubled), or 1 mole H2 with 0.5 moles O2 makes 1 mole H2O (halved)—the 2:1:2 ratio is preserved! In the given equation $\mathrm{N_2 + 3H_2 \rightarrow 2NH_3}$ , the coefficient of H2 is 3 and N2 is 1 (implied), so for 1 mole of N2, 3 moles of H2 are required, directly from the 1:3 ratio of N2 to H2. Choice C correctly interprets the coefficients as the mole ratio between the specified substances. Choice A might result if you misread the coefficient of H2 as 1, but remember to always check the numbers explicitly written or implied! Reading mole ratios from balanced equations: (1) Locate the two substances you're comparing in the equation. (2) Read their coefficients (the numbers in front—if no number is written, the coefficient is 1). (3) Write the ratio: [coefficient of first substance] : [coefficient of second substance]. Example: from $\mathrm{N_2 + 3H_2 \rightarrow 2NH_3}$ , the ratio of N2 to H2 is 1:3 (read coefficients 1 and 3). The ratio of H2 to NH3 is 3:2 (coefficients 3 and 2). The ratio of N2 to NH3 is 1:2 (coefficients 1 and 2). You can find the ratio between ANY two substances in the equation by reading their coefficients! Using mole ratios as conversion factors: mole ratios let you predict amounts! If you know how many moles of one substance you have, you can calculate moles of another using the ratio. From $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$ , if you have 5 moles of H2, how many moles H2O can form? Ratio H2:H2O is 2:2 or 1:1, so 5 moles H2 produces 5 moles H2O. If you have 5 moles H2, how many moles O2 needed? Ratio H2:O2 is 2:1, so 5 moles H2 needs 2.5 moles O2. The coefficients are your conversion tool—they're not just decorative numbers, they're the mathematical relationship between substances in the reaction!

Question 2

Propane combusts according to the balanced equation $\mathrm{C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O}$ . What is the mole ratio of $\mathrm{CO_2}$ produced to $\mathrm{C_3H_8}$ consumed?

$1:3$
$3:1$ (correct answer)
$3:8$
$5:1$

Explanation: This question tests your understanding that coefficients in balanced chemical equations represent mole ratios—the proportional relationships between amounts of reactants consumed and products formed in a chemical reaction. The coefficients in a balanced equation (the numbers in front of chemical formulas) tell you the ratio of MOLES of each substance involved in the reaction: in $2\mathrm{H_2} + \mathrm{O_2} \rightarrow 2\mathrm{H_2O}$ , the coefficients 2, 1, and 2 mean that 2 moles of hydrogen gas react with 1 mole of oxygen gas to produce 2 moles of water. This ratio is the fundamental relationship—it means for every 1 mole of $\mathrm{O_2}$ consumed, exactly 2 moles of $\mathrm{H_2}$ are consumed and exactly 2 moles of $\mathrm{H_2O}$ are produced. The ratio stays constant no matter how much you scale it: 4 moles $\mathrm{H_2}$ with 2 moles $\mathrm{O_2}$ makes 4 moles $\mathrm{H_2O}$ (doubled), or 1 mole $\mathrm{H_2}$ with 0.5 moles $\mathrm{O_2}$ makes 1 mole $\mathrm{H_2O}$ (halved)—the $2:1:2$ ratio is preserved! In the given equation $\mathrm{C_3H_8} + 5\mathrm{O_2} \rightarrow 3\mathrm{CO_2} + 4\mathrm{H_2O}$ , the coefficient for $\mathrm{CO_2}$ is 3 and for $\mathrm{C_3H_8}$ is 1 (implied), so the mole ratio of $\mathrm{CO_2}$ produced to $\mathrm{C_3H_8}$ consumed is $3:1$ , meaning 3 moles of $\mathrm{CO_2}$ from 1 mole of $\mathrm{C_3H_8}$ . Choice B correctly interprets the coefficients as the mole ratio between the specified substances. A distractor like choice C might pull in unrelated coefficients like $3:8$ from subscripts, but ratios are from coefficients only, not subscripts or other numbers. Reading mole ratios from balanced equations: (1) Locate the two substances you're comparing in the equation. (2) Read their coefficients (the numbers in front—if no number is written, the coefficient is 1). (3) Write the ratio: [coefficient of first substance] : [coefficient of second substance]. Using mole ratios as conversion factors: mole ratios let you predict amounts! If you know how many moles of one substance you have, you can calculate moles of another using the ratio—they're not just decorative numbers, they're the mathematical relationship between substances in the reaction!

Question 3

In the balanced equation $\mathrm{4Fe + 3O_2 \rightarrow 2Fe_2O_3}$ what is the mole ratio of oxygen gas ( $\mathrm{O_2}$ ) to iron(III) oxide ( $\mathrm{Fe_2O_3}$ )?

$3:2$ (correct answer)
$2:3$
$3:4$
$6:2$

Question 4

Iron reacts with chlorine to form iron(III) chloride: $\mathrm{2Fe + 3Cl_2 \rightarrow 2FeCl_3}$ . What is the mole ratio of $\mathrm{Fe}$ to $\mathrm{Cl_2}$ ?

$3:2$
$2:3$ (correct answer)
$2:1$
$1:3$

Explanation: This question tests your understanding that coefficients in balanced chemical equations represent mole ratios—the proportional relationships between amounts of reactants consumed and products formed in a chemical reaction. The coefficients in a balanced equation (the numbers in front of chemical formulas) tell you the ratio of MOLES of each substance involved in the reaction: in $2\mathrm{H_2} + \mathrm{O_2} \rightarrow 2\mathrm{H_2O}$ , the coefficients 2, 1, and 2 mean that 2 moles of hydrogen gas react with 1 mole of oxygen gas to produce 2 moles of water. This ratio is the fundamental relationship—it means for every 1 mole of O2 consumed, exactly 2 moles of H2 are consumed and exactly 2 moles of H2O are produced. The ratio stays constant no matter how much you scale it: 4 moles H2 with 2 moles O2 makes 4 moles H2O (doubled), or 1 mole H2 with 0.5 moles O2 makes 1 mole H2O (halved)—the 2:1:2 ratio is preserved! In the given equation $2\mathrm{Fe} + 3\mathrm{Cl_2} \rightarrow 2\mathrm{FeCl_3}$ , the coefficient for Fe is 2 and for Cl2 is 3, so the mole ratio of Fe to Cl2 is 2:3, meaning 2 moles of Fe react with 3 moles of Cl2. Choice B correctly interprets the coefficients as the mole ratio between the specified substances. A distractor like choice A might swap to 3:2, but ensure you list in the asked order—Fe to Cl2 means coefficient of Fe first (2) to Cl2 (3). Reading mole ratios from balanced equations: (1) Locate the two substances you're comparing in the equation. (2) Read their coefficients (the numbers in front—if no number is written, the coefficient is 1). (3) Write the ratio: [coefficient of first substance] : [coefficient of second substance]. Using mole ratios as conversion factors: mole ratios let you predict amounts! If you know how many moles of one substance you have, you can calculate moles of another using the ratio—they're not just decorative numbers, they're the mathematical relationship between substances in the reaction!

Question 5

In the balanced equation $\mathrm{Zn + 2HCl \rightarrow ZnCl_2 + H_2}$ how many moles of $\mathrm{HCl}$ are required to react with $1$ mol of $\mathrm{Zn}$ ?

$1$ mol
$2$ mol (correct answer)
$3$ mol
$4$ mol

Explanation: This question tests your understanding that coefficients in balanced chemical equations represent mole ratios—the proportional relationships between amounts of reactants consumed and products formed in a chemical reaction. The coefficients in a balanced equation (the numbers in front of chemical formulas) tell you the ratio of MOLES of each substance involved in the reaction: in $2\mathrm{H_2 + O_2 \rightarrow 2H_2O}$ , the coefficients 2, 1, and 2 mean that 2 moles of hydrogen gas react with 1 mole of oxygen gas to produce 2 moles of water. This ratio is the fundamental relationship—it means for every 1 mole of O2 consumed, exactly 2 moles of H2 are consumed and exactly 2 moles of H2O are produced. The ratio stays constant no matter how much you scale it: 4 moles H2 with 2 moles O2 makes 4 moles H2O (doubled), or 1 mole H2 with 0.5 moles O2 makes 1 mole H2O (halved)—the $2:1:2$ ratio is preserved! In the given equation $\mathrm{Zn + 2HCl \rightarrow ZnCl_2 + H_2}$ , the coefficient of HCl is 2 and Zn is 1 (implied), so 2 moles of HCl are required for 1 mole of Zn, based on the $1:2$ ratio of Zn to HCl. Choice B correctly interprets the coefficients as the mole ratio between the specified substances. Choice A could be a mistake if you ignore the coefficient of HCl, but always include the numbers—it's 2, not 1! Reading mole ratios from balanced equations: (1) Locate the two substances you're comparing in the equation. (2) Read their coefficients (the numbers in front—if no number is written, the coefficient is 1). (3) Write the ratio: [coefficient of first substance] : [coefficient of second substance]. Example: from $\mathrm{N_2 + 3H_2 \rightarrow 2NH_3}$ , the ratio of N2 to H2 is $1:3$ (read coefficients 1 and 3). The ratio of H2 to NH3 is $3:2$ (coefficients 3 and 2). The ratio of N2 to NH3 is $1:2$ (coefficients 1 and 2). You can find the ratio between ANY two substances in the equation by reading their coefficients! Using mole ratios as conversion factors: mole ratios let you predict amounts! If you know how many moles of one substance you have, you can calculate moles of another using the ratio. From $2\mathrm{H_2 + O_2 \rightarrow 2H_2O}$ , if you have 5 moles of H2, how many moles H2O can form? Ratio H2:H2O is $2:2$ or $1:1$ , so 5 moles H2 produces 5 moles H2O. If you have 5 moles H2, how many moles O2 needed? Ratio H2:O2 is $2:1$ , so 5 moles H2 needs 2.5 moles O2. The coefficients are your conversion tool—they're not just decorative numbers, they're the mathematical relationship between substances in the reaction!

Question 6

Iron(III) chloride forms by the balanced synthesis equation $\mathrm{2Fe + 3Cl_2 \rightarrow 2FeCl_3}$ What is the mole ratio of $\mathrm{Fe}$ to $\mathrm{Cl_2}$ ?

$3:2$
$2:3$ (correct answer)
$2:6$
$1:1$

Explanation: This question tests your understanding that coefficients in balanced chemical equations represent mole ratios—the proportional relationships between amounts of reactants consumed and products formed in a chemical reaction. The coefficients in a balanced equation (the numbers in front of chemical formulas) tell you the ratio of MOLES of each substance involved in the reaction: in $2\mathrm{H_2} + \mathrm{O_2} \rightarrow 2\mathrm{H_2O}$ , the coefficients 2, 1, and 2 mean that 2 moles of hydrogen gas react with 1 mole of oxygen gas to produce 2 moles of water. This ratio is the fundamental relationship—it means for every 1 mole of O2 consumed, exactly 2 moles of H2 are consumed and exactly 2 moles of H2O are produced. The ratio stays constant no matter how much you scale it: 4 moles H2 with 2 moles O2 makes 4 moles H2O (doubled), or 1 mole H2 with 0.5 moles O2 makes 1 mole H2O (halved)—the $2:1:2$ ratio is preserved! In the given equation $2\mathrm{Fe} + 3\mathrm{Cl_2} \rightarrow 2\mathrm{FeCl_3}$ , the coefficient of Fe is 2 and Cl2 is 3, so the mole ratio of Fe to Cl2 is $2:3$ , meaning 2 moles of Fe react with 3 moles of Cl2. Choice B correctly interprets the coefficients as the mole ratio between the specified substances. Choice A might happen if you swap the order, but the question asks for Fe to Cl2, which is $2:3$ , not $3:2$ —double-check the sequence! Reading mole ratios from balanced equations: (1) Locate the two substances you're comparing in the equation. (2) Read their coefficients (the numbers in front—if no number is written, the coefficient is 1). (3) Write the ratio: [coefficient of first substance] : [coefficient of second substance]. Example: from $\mathrm{N_2} + 3\mathrm{H_2} \rightarrow 2\mathrm{NH_3}$ , the ratio of N2 to H2 is $1:3$ (read coefficients 1 and 3). The ratio of H2 to NH3 is $3:2$ (coefficients 3 and 2). The ratio of N2 to NH3 is $1:2$ (coefficients 1 and 2). You can find the ratio between ANY two substances in the equation by reading their coefficients! Using mole ratios as conversion factors: mole ratios let you predict amounts! If you know how many moles of one substance you have, you can calculate moles of another using the ratio. From $2\mathrm{H_2} + \mathrm{O_2} \rightarrow 2\mathrm{H_2O}$ , if you have 5 moles of H2, how many moles H2O can form? Ratio H2:H2O is $2:2$ or $1:1$ , so 5 moles H2 produces 5 moles H2O. If you have 5 moles H2, how many moles O2 needed? Ratio H2:O2 is $2:1$ , so 5 moles H2 needs 2.5 moles O2. The coefficients are your conversion tool—they're not just decorative numbers, they're the mathematical relationship between substances in the reaction!

Question 7

In the balanced combustion equation $\mathrm{CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O}$ what is the mole ratio of $\mathrm{O_2}$ to $\mathrm{CH_4}$ ?

$2:1$ (correct answer)
$1:2$
$2:4$
$4:2$

Explanation: This question tests your understanding that coefficients in balanced chemical equations represent mole ratios—the proportional relationships between amounts of reactants consumed and products formed in a chemical reaction. The coefficients in a balanced equation (the numbers in front of chemical formulas) tell you the ratio of MOLES of each substance involved in the reaction: in 2H2 + O2 → 2H2O, the coefficients 2, 1, and 2 mean that 2 moles of hydrogen gas react with 1 mole of oxygen gas to produce 2 moles of water. This ratio is the fundamental relationship—it means for every 1 mole of O2 consumed, exactly 2 moles of H2 are consumed and exactly 2 moles of H2O are produced. The ratio stays constant no matter how much you scale it: 4 moles H2 with 2 moles O2 makes 4 moles H2O (doubled), or 1 mole H2 with 0.5 moles O2 makes 1 mole H2O (halved)—the 2:1:2 ratio is preserved! In the given equation CH4 + 2O2 → CO2 + 2H2O, the coefficient of O2 is 2 and CH4 is 1 (implied), so the mole ratio of O2 to CH4 is 2:1, meaning 2 moles of O2 are needed for every 1 mole of CH4. Choice A correctly interprets the coefficients as the mole ratio between the specified substances. Choice B might tempt you if you reverse the order, but remember, the ratio is O2 to CH4, not CH4 to O2—always list them in the order asked! Reading mole ratios from balanced equations: (1) Locate the two substances you're comparing in the equation. (2) Read their coefficients (the numbers in front—if no number is written, the coefficient is 1). (3) Write the ratio: [coefficient of first substance] : [coefficient of second substance]. Example: from N2 + 3H2 → 2NH3, the ratio of N2 to H2 is 1:3 (read coefficients 1 and 3). The ratio of H2 to NH3 is 3:2 (coefficients 3 and 2). The ratio of N2 to NH3 is 1:2 (coefficients 1 and 2). You can find the ratio between ANY two substances in the equation by reading their coefficients! Using mole ratios as conversion factors: mole ratios let you predict amounts! If you know how many moles of one substance you have, you can calculate moles of another using the ratio. From 2H2 + O2 → 2H2O, if you have 5 moles of H2, how many moles H2O can form? Ratio H2:H2O is 2:2 or 1:1, so 5 moles H2 produces 5 moles H2O. If you have 5 moles H2, how many moles O2 needed? Ratio H2:O2 is 2:1, so 5 moles H2 needs 2.5 moles O2. The coefficients are your conversion tool—they're not just decorative numbers, they're the mathematical relationship between substances in the reaction!

Question 8

Rust formation (simplified) can be represented by the balanced equation $\mathrm{4Fe + 3O_2 \rightarrow 2Fe_2O_3}$ . What is the mole ratio of $\mathrm{Fe}$ to $\mathrm{Fe_2O_3}$ ?

$2:4$
$4:2$ (correct answer)
$3:2$
$2:3$

Explanation: This question tests your understanding that coefficients in balanced chemical equations represent mole ratios—the proportional relationships between amounts of reactants consumed and products formed in a chemical reaction. The coefficients in a balanced equation (the numbers in front of chemical formulas) tell you the ratio of MOLES of each substance involved in the reaction: in $2\mathrm{H_2} + \mathrm{O_2} \rightarrow 2\mathrm{H_2O}$ , the coefficients 2, 1, and 2 mean that 2 moles of hydrogen gas react with 1 mole of oxygen gas to produce 2 moles of water. This ratio is the fundamental relationship—it means for every 1 mole of $\mathrm{O_2}$ consumed, exactly 2 moles of $\mathrm{H_2}$ are consumed and exactly 2 moles of $\mathrm{H_2O}$ are produced. The ratio stays constant no matter how much you scale it: 4 moles $\mathrm{H_2}$ with 2 moles $\mathrm{O_2}$ makes 4 moles $\mathrm{H_2O}$ (doubled), or 1 mole $\mathrm{H_2}$ with 0.5 moles $\mathrm{O_2}$ makes 1 mole $\mathrm{H_2O}$ (halved)—the 2:1:2 ratio is preserved! In the given equation $4\mathrm{Fe} + 3\mathrm{O_2} \rightarrow 2\mathrm{Fe_2O_3}$ , the coefficient for Fe is 4 and for Fe2O3 is 2, so the mole ratio of Fe to Fe2O3 is 4:2, meaning 4 moles of Fe produce 2 moles of Fe2O3. Choice B correctly interprets the coefficients as the mole ratio between the specified substances. A distractor like choice A might reverse to 2:4, but list in the order asked—Fe to Fe2O3 means coefficient of Fe first (4) to Fe2O3 (2). Reading mole ratios from balanced equations: (1) Locate the two substances you're comparing in the equation. (2) Read their coefficients (the numbers in front—if no number is written, the coefficient is 1). (3) Write the ratio: [coefficient of first substance] : [coefficient of second substance]. Using mole ratios as conversion factors: mole ratios let you predict amounts! If you know how many moles of one substance you have, you can calculate moles of another using the ratio—they're not just decorative numbers, they're the mathematical relationship between substances in the reaction!

Question 9

Ammonia forms according to $\text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3.$ What is the mole ratio of $\text{NH}_3$ to $\text{H}_2$ ?

2:3 (correct answer)
3:2
2:1
3:1

Explanation: This question tests your understanding that coefficients in balanced chemical equations represent mole ratios—the proportional relationships between amounts of reactants consumed and products formed in a chemical reaction. The coefficients in a balanced equation (the numbers in front of chemical formulas) tell you the ratio of MOLES of each substance involved in the reaction: in $\text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3$ , the coefficients 1, 3, and 2 mean that 1 mole of nitrogen reacts with 3 moles of hydrogen to produce 2 moles of ammonia. This ratio is the fundamental relationship—it means for every 3 moles of $\text{H}_2$ consumed, exactly 1 mole of $\text{N}_2$ is consumed and 2 moles of $\text{NH}_3$ are produced. The ratio stays constant no matter how much you scale it: 2 moles of $\text{N}_2$ with 6 moles of $\text{H}_2$ makes 4 moles of $\text{NH}_3$ (doubled), or 0.5 moles of $\text{N}_2$ with 1.5 moles of $\text{H}_2$ makes 1 mole of $\text{NH}_3$ (halved)—the 1:3:2 ratio is preserved! In this equation, the mole ratio of $\text{NH}_3$ to $\text{H}_2$ is extracted from their coefficients: $\text{NH}_3$ has 2 and $\text{H}_2$ has 3, so it's 2:3, meaning 2 moles of $\text{NH}_3$ per 3 moles of $\text{H}_2$ . Choice A correctly interprets the coefficients as the mole ratio between $\text{NH}_3$ and $\text{H}_2$ , stating 2:3. A distractor like choice B (3:2) might swap the order, but the question specifies $\text{NH}_3$ to $\text{H}_2$ , which is 2:3—pay attention to which comes first. Reading mole ratios from balanced equations: (1) Locate the two substances you're comparing in the equation. (2) Read their coefficients (the numbers in front—if no number is written, the coefficient is 1). (3) Write the ratio: [coefficient of first substance] : [coefficient of second substance]. Using mole ratios as conversion factors: mole ratios let you predict amounts! If you know how many moles of one substance you have, you can calculate moles of another using the ratio.

Question 10

Methane combusts according to $\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}.$ What is the mole ratio of $\text{H}_2\text{O}$ to $\text{CO}_2$ ?

2:1 (correct answer)
1:2
2:2
1:1

Explanation: This question tests your understanding that coefficients in balanced chemical equations represent mole ratios—the proportional relationships between amounts of reactants consumed and products formed in a chemical reaction. The coefficients in a balanced equation (the numbers in front of chemical formulas) tell you the ratio of MOLES of each substance involved in the reaction: in $\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}$ , the coefficients 1, 2, 1, and 2 mean that 1 mole of $\text{CH}_4$ reacts with 2 moles of $\text{O}_2$ to produce 1 mole of $\text{CO}_2$ and 2 moles of $\text{H}_2\text{O}$ . This ratio is the fundamental relationship—it means for every 1 mole of $\text{CO}_2$ produced, exactly 2 moles of $\text{H}_2\text{O}$ are also produced. The ratio stays constant no matter how much you scale it: 2 moles $\text{CH}_4$ with 4 moles $\text{O}_2$ makes 2 moles $\text{CO}_2$ and 4 moles $\text{H}_2\text{O}$ (doubled), or 0.5 moles $\text{CH}_4$ with 1 mole $\text{O}_2$ makes 0.5 moles $\text{CO}_2$ and 1 mole $\text{H}_2\text{O}$ (halved)—the 1:2:1:2 ratio is preserved! In this equation, the mole ratio of $\text{H}_2\text{O}$ to $\text{CO}_2$ is extracted from their coefficients: $\text{H}_2\text{O}$ has 2 and $\text{CO}_2$ has 1 (implied), so it's 2:1, meaning 2 moles of $\text{H}_2\text{O}$ per 1 mole of $\text{CO}_2$ . Choice A correctly interprets the coefficients as the mole ratio between $\text{H}_2\text{O}$ and $\text{CO}_2$ , stating 2:1. A distractor like choice B (1:2) could be from reversing the substances, but the question asks for $\text{H}_2\text{O}$ to $\text{CO}_2$ —keep the order straight. Reading mole ratios from balanced equations: (1) Locate the two substances you're comparing in the equation. (2) Read their coefficients (the numbers in front—if no number is written, the coefficient is 1). (3) Write the ratio: [coefficient of first substance] : [coefficient of second substance]. Using mole ratios as conversion factors: mole ratios let you predict amounts! If you know how many moles of one substance you have, you can calculate moles of another using the ratio.