Understand Ratio Concept and Language - 6th Grade Math

What is a ratio?

A comparison of two quantities by division. Ratios show how quantities relate through division.
What does the ratio $3:5$ mean using "for every" ratio language?

For every $3$ of the first quantity, there are $5$ of the second. Ratio language describes the relationship between quantities.
Identify the ratio described: "For every $1$ vote for A, C gets $3$ votes."

$1:3$ (A:C). Direct translation of the voting relationship.
What is the ratio of beaks to wings if there are $18$ wings and $9$ beaks?

$1:2$ . Reverse the order: beaks first, then wings.
What is the ratio of $\frac{3}{4}$ cup to $\frac{1}{2}$ cup in simplest form?

$3:2$ . Convert to common denominator: $\frac{3}{4}:\frac{2}{4} = 3:2$ .
What is the ratio of $0.6$ liters to $1.5$ liters in simplest form?

$2:5$ . Multiply by 10 to get $6:15$ , then divide by 3.
What is the ratio of $10$ minutes to $2$ hours after converting to the same unit?

$1:12$ . Convert hours to minutes: $10:120$ , then simplify by 10.
Choose the correct ratio: $10$ blue tiles and $6$ green tiles; blue to green.

$5:3$ . Simplify $10:6$ by dividing both by $2$ .
What is the ratio of $24$ minutes to $2$ hours when both are in minutes?

$24:120$ . Convert $2$ hours to $120$ minutes first.
What is the ratio of $8$ apples to $2$ oranges written as a fraction in simplest form?

$\frac{4}{1}$ . Simplify $\frac{8}{2}$ by dividing both by $2$ .
What is the ratio $9:12$ in simplest form?

$3:4$ . Divide both by GCF of 3: $\frac{9}{3}:\frac{12}{3} = 3:4$ .
Which order matches "the ratio of cats to dogs" if there are $4$ cats and $7$ dogs?

$4:7$ . Order matters: first quantity comes first in the ratio.
Which ratio matches $5$ boys and $9$ girls written as $\text{girls:boys}$ ?

$9:5$ . Girls first, then boys, following the stated order.
What is the ratio of $14$ total students to $8$ students in band written as $\text{total:band}$ in simplest form?

$7:4$ . Divide both by GCF of 2: $\frac{14}{2}:\frac{8}{2} = 7:4$ .
What does the ratio $a:b$ mean in words?

$a$ units for every $b$ units. Describes the relationship between two quantities.
What is the ratio of $15$ red marbles to $5$ blue marbles written as $\text{red:blue}$ in simplest form?

$3:1$ . Divide both by GCF of 5: $\frac{15}{5}:\frac{5}{5} = 3:1$ .
What is the unit rate meaning of the ratio $\frac{12 \text{miles}}{3 \text{hours}}$ ?

$4$ miles per $1$ hour. Divide to find the rate: $12 \div 3 = 4$ miles per hour.
What are three common ways to write the ratio of $a$ to $b$ ?

$a:b$ , $a$ to $b$ , and $\frac{a}{b}$ . These are the three standard ratio notations.
What is the ratio of $7$ triangles to $21$ circles written as $\text{triangles:circles}$ in simplest form?

$1:3$ . Divide both by GCF of 7: $\frac{7}{7}:\frac{21}{7} = 1:3$ .
What is a ratio, in words, comparing two quantities?

A comparison of two quantities by division. Ratios show how quantities relate through division.
Find the missing number: The ratio $x:6$ is equivalent to $4:3$ .

$x=8$ . Cross multiply: $3x = 24$ , so $x = 8$ .
Find and correct the ratio error: " $8$ cats and $6$ dogs gives dogs:cats $=8:6$ ."

Correct dogs:cats is $6:8$ (simplifies to $3:4$ ). Order was reversed; dogs:cats should be $6:8$ .
Identify the ratio described: "For every $4$ apples, there are $3$ oranges."

$4:3$ (apples:oranges). Direct translation of the given relationship.
What does the ratio $2:1$ mean using "for every" language?

For every $2$ of the first quantity, there is $1$ of the second. The first quantity appears twice for each second quantity.
Which order matches "the ratio of cats to dogs"?

Cats first, then dogs. Order matters: first quantity comes first in the ratio.
What ratio (in simplest form) represents $12$ red marbles to $8$ blue marbles?

$3:2$ . Divide both by their GCD: $12÷4=3$ , $8÷4=2$ .
What is the ratio of $24$ minutes to $2$ hours in simplest form?

$1:5$ . Simplify $24:120$ by dividing both by $24$ .
Find the missing number: The ratio $9:y$ is equivalent to $3:5$ .

$y=15$ . Cross multiply: $3y = 45$ , so $y = 15$ .
Which statement correctly matches the ratio $5:2$ ?

For every $5$ of the first quantity, there are $2$ of the second. This describes the multiplicative relationship.
Which statement correctly matches the ratio $2:5$ ?

For every $2$ of the first quantity, there are $5$ of the second. The ratio $2:5$ means 2 units to 5 units.
What is the ratio of $12$ girls to $8$ boys written as $\text{girls:boys}$ in simplest form?

$3:2$ . Divide both by GCF of 4: $\frac{12}{4}:\frac{8}{4} = 3:2$ .
Identify the error: Writing "ratio of dogs to cats" as $\frac{\text{cats}}{\text{dogs}}$ .

The order is reversed; it should be $\frac{\text{dogs}}{\text{cats}}$ . Ratio order must match the stated comparison.
What three notations can represent the ratio of $a$ to $b$ ?

$a:b$ , $a$ to $b$ , and $\frac{a}{b}$ . Three standard ways to write ratios mathematically.
What ratio (in simplest form) represents $15$ girls to $20$ boys?

$3:4$ . Divide both by their GCD: $15÷5=3$ , $20÷5=4$ .
What is the ratio $4:6$ written as a fraction in simplest form?

$\frac{2}{3}$ . Write as fraction and simplify by dividing by 2.
Identify the ratio of wings to beaks if there are $18$ wings and $9$ beaks.

$2:1$ . Simplify $18:9$ by dividing both by $9$ .
What is the ratio $18$ meters to $24$ meters written as a fraction in simplest form?

$\frac{3}{4}$ . Simplify by dividing both by GCF of 6: $\frac{18÷6}{24÷6} = \frac{3}{4}$ .
What is the ratio of shaded to unshaded squares if $6$ are shaded and $14$ are unshaded, in simplest form?

$3:7$ . Simplify $6:14$ by dividing both by $2$ .
What does "Candidate C received nearly three votes for every vote Candidate A received" mean as a ratio $C:A$ ?

$3:1$ (approximately). "Nearly three" means approximately $3$ to $1$ .
What is the ratio of $3$ feet to $18$ inches after converting to the same unit?

$2:1$ . Convert feet to inches: $36:18$ , then simplify by 18.

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