Add Tenths and Hundredths - 4th Grade Math

1. Josh walked $\frac{4}{10}$ of a mile to school, then $\frac{35}{100}$ of a mile to the library after school. Which expression correctly shows the total distance Josh walked?
   Answer: $\frac{40 + 35}{100} = \frac{75}{100}$ mile Convert $\frac{4}{10}$ to $\frac{40}{100}$, then add: $\frac{40}{100} + \frac{35}{100} = \frac{75}{100}$. Choice A incorrectly adds denominators. Choice C fails to convert tenths to hundredths. Choice D incorrectly converts the second fraction to tenths instead of the first to hundredths.
2. Two athletes are training for a race. On Saturday, athlete A ran $\frac{9}{10}$ of the total course and athlete B ran $\frac{55}{100}$ of the total course. How much more of the course did athlete A complete than athlete B?
   Answer: Athlete A ran $\frac{35}{100}$ more of the course than athlete B When you need to find how much more one fraction is than another, you're looking for the difference between them. This means you need to subtract the smaller fraction from the larger one. First, you need to compare $\frac{9}{10}$ and $\frac{55}{100}$. To subtract fractions, they must have the same denominator. Since $\frac{9}{10} = \frac{90}{100}$, you can now see that athlete A ran $\frac{90}{100}$ of the course while athlete B ran $\frac{55}{100}$. To find how much more athlete A ran, subtract: $\frac{90}{100} - \frac{55}{100} = \frac{35}{100}$. This makes C the correct answer. Let's examine why the other answers are wrong. Choice A ($\frac{54}{100}$) likely comes from subtracting $\frac{55}{100} - \frac{9}{100}$ instead of converting $\frac{9}{10}$ to hundredths first. Choice B ($\frac{46}{100}$) might result from incorrectly converting $\frac{9}{10}$ or making an arithmetic error during subtraction. Choice D ($\frac{145}{100}$) comes from adding the fractions instead of subtracting them ($\frac{90}{100} + \frac{55}{100} = \frac{145}{100}$). Remember: When comparing fractions, always convert them to the same denominator first. Look for key words like "how much more" or "difference" – these signal subtraction problems. Take your time converting fractions and double-check that you're performing the right operation.
3. A garden has two sections. The vegetable section covers $\frac{5}{10}$ of the garden and the flower section covers $\frac{18}{100}$ of the garden. The rest is grass. What fraction represents the grass area?
   Answer: $\frac{32}{100}$ $\frac{32}{100}$ is correct because the vegetable and flower sections together cover $\frac{68}{100}$ of the garden, and $1 - \frac{68}{100} = \frac{32}{100}$. $\frac{23}{100}$ is incorrect because it results from a subtraction slip. $\frac{68}{100}$ is incorrect because it is the combined vegetable and flower area, not the remaining grass. $\frac{77}{100}$ is incorrect because it does not match the correct total.
4. A craft project requires three materials. Ribbon uses $\frac{1}{10}$ of the budget, beads use $\frac{42}{100}$ of the budget, and fabric uses the remaining amount. If the total budget is exactly used up, what fraction of the budget is spent on fabric?
   Answer: Fabric costs $\frac{48}{100}$ of the total project budget Convert $\frac{1}{10} = \frac{10}{100}$. Add known costs: $\frac{10}{100} + \frac{42}{100} = \frac{52}{100}$. Subtract from total budget: $\frac{100}{100} - \frac{52}{100} = \frac{48}{100}$. Choice A adds 1 + 42 = 43 without converting. Choice C shows the combined cost of ribbon and beads. Choice D incorrectly adds all three materials as 10 + 42 + 5 = 57.
5. Sofia has $\frac{6}{10}$ of a dollar in dimes and $\frac{8}{100}$ of a dollar in pennies. Convert $\frac{6}{10}$ to hundredths: $\frac{6}{10}=\frac{60}{100}$. Then add: $\frac{60}{100}+\frac{8}{100}=\frac{\square}{100}$. What fraction of a dollar does she have?
   Answer: $\frac{68}{100}$ This question tests 4th grade ability to express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (CCSS.4.NF.5). To add fractions with denominators 10 and 100, we must first convert to a common denominator—$100 = 10 \times 10$. The key relationship: $\frac{1}{10} = \frac{10}{100}$ (one tenth equals ten hundredths), so any fraction $\frac{a}{10} = \frac{10a}{100}$ by multiplying numerator and denominator by 10. Once both fractions have denominator 100, add the numerators and keep the denominator: $\frac{10a}{100} + \frac{b}{100} = \frac{10a + b}{100}$. To add $\frac{6}{10} + \frac{8}{100}$, first convert $\frac{6}{10}$ to hundredths: $\frac{6}{10} = \frac{6 \times 10}{100} = \frac{60}{100}$. Then add: $\frac{60}{100} + \frac{8}{100} = \frac{60 + 8}{100} = \frac{68}{100}$. You can also think decimally: $\frac{6}{10} = 0.6$, $\frac{8}{100} = 0.08$, sum = $0.68$. Choice A is correct because converting $\frac{6}{10}$: multiply numerator $6 \times 10 = 60$, denominator $10 \times 10 = 100$, giving $\frac{60}{100}$; then adding: $\frac{60}{100} + \frac{8}{100}$, add numerators: $60 + 8 = 68$, keep denominator 100: $\frac{68}{100}$. This demonstrates understanding that tenths must be expressed as hundredths before adding. Choice B represents adding without converting (added $6+8=14$ directly), which happens when students don't recognize need for common denominator. To help students: Visualize with hundredths grid ($10\times10$ squares)—each COLUMN is $\frac{1}{10} = 10$ squares, each SQUARE is $\frac{1}{100}$. To convert tenths to hundredths, multiply numerator by 10: $\frac{6}{10} = \frac{6\times10}{100} = \frac{60}{100}$. Check: count squares ($60$ squares for 6 columns). Then add: $\frac{60}{100} + \frac{8}{100} = \frac{68}{100}$ ($60 + 8 = 68$ squares total). Connect to decimals: $\frac{6}{10} = 0.6$ (six tenths), $\frac{8}{100} = 0.08$ (eight hundredths), $0.6 + 0.08 = 0.68$ (sixty-eight hundredths) = $\frac{68}{100}$. Use money: 6 dimes ($\frac{6}{10}$ dollar) = 60 pennies ($\frac{60}{100}$ dollar), plus 8 pennies = 68 pennies = $\frac{68}{100}$ dollar. Pattern: $\frac{1}{10}=\frac{10}{100}$, $\frac{2}{10}=\frac{20}{100}$, $\frac{6}{10}=\frac{60}{100}$ (multiply numerator by 10). Watch for: not converting tenths to hundredths before adding, multiplying by wrong number, arithmetic errors, and adding denominators.
6. A recipe calls for $\frac{3}{10}$ cup of sugar and $\frac{45}{100}$ cup of flour. How much more flour than sugar does the recipe require?
   Answer: $\frac{15}{100}$ cup more flour than sugar Convert sugar to hundredths: $\frac{3}{10} = \frac{30}{100}$. Find the difference: $\frac{45}{100} - \frac{30}{100} = \frac{15}{100}$. Choice B subtracts incorrectly (45 - 3 = 42). Choice C adds instead of subtracting (45 + 3 = 48). Choice D adds the total amount (45 + 30 = 75).
7. What is $\frac{8}{10} + \frac{9}{100}$?
   Answer: $\frac{89}{100}$ The correct answer is A, 89/100. Rewriting 8/10 as 80/100 and adding gives 80/100 + 9/100 = 89/100. Choice B, 17/100, comes from adding just the numerators of the original fractions without converting to a common denominator. Choice C, 80/100, is only the converted first fraction, not the final sum. Choice D, 99/100, comes from an addition error.
8. Jamal wrote $\frac{5}{10}+\frac{23}{100}$. He knows he must use a common denominator of 100. Convert: $\frac{5}{10}=\frac{50}{100}$. Add: $\frac{50}{100}+\frac{23}{100}=\frac{\square}{100}$. What is the sum?
   Answer: $\frac{73}{100}$ Choice C is correct because 50/100 plus 23/100 equals 73/100. Choice A is incorrect because it does not correctly add the two numerators. Choice B is incorrect because it is close to the correct sum but reflects an addition error of one hundredth. Choice D is incorrect because it only repeats the converted first fraction without adding the second.
9. Add $\frac{9}{10} + \frac{4}{100}$. First, convert: $\frac{9}{10} = \frac{90}{100}$. Then add: $\frac{90}{100} + \frac{4}{100} = \frac{90+4}{100}$. What is the sum?
   Answer: $\frac{94}{100}$ The correct answer is D, $\frac{94}{100}$, because $\frac{90}{100} + \frac{4}{100} = \frac{94}{100}$. Choice A comes from adding 9 + 4 directly without converting to a common denominator first. Choice B comes from mistakenly adding an extra 10 to the numerator. Choice C stops after converting $\frac{9}{10}$ and forgets to add the $\frac{4}{100}$.
10. Add: $\frac{7}{10} + \frac{6}{100}$. What is the sum?
    Answer: $\frac{76}{100}$ $\frac{76}{100}$ is correct because $\frac{7}{10} = \frac{70}{100}$, and $\frac{70}{100} + \frac{6}{100} = \frac{76}{100}$. $\frac{13}{100}$ is incorrect because it adds the numerators without converting to a common denominator. $\frac{77}{100}$ is incorrect because it is off by one from the correct sum. $\frac{70}{100}$ is incorrect because it only represents the converted first fraction.
11. What is $\frac{9}{10} + \frac{5}{100}$?
    Answer: $\frac{95}{100}$ Rewrite $\frac{9}{10}$ with denominator 100: $\frac{9}{10} = \frac{90}{100}$. Then add: $\frac{90}{100} + \frac{5}{100} = \frac{95}{100}$. Choice B adds only the original numerators without converting first ($9+5=14$). Choice C miscalculates $90+5$. Choice D repeats the converted value of $\frac{9}{10}$ without adding $\frac{5}{100}$.
12. Add $\frac{3}{10}+\frac{4}{100}$. First, convert $\frac{3}{10}$ to an equivalent fraction with denominator 100: $\frac{3}{10}=\frac{30}{100}$. Then add: $\frac{30}{100}+\frac{4}{100}=\frac{\square}{100}$. What is the sum?
    Answer: $\frac{34}{100}$ Converting 3/10 to hundredths gives 30/100, and adding 30/100 plus 4/100 gives 34/100, making Choice B correct. Choice A, 7/100, comes from adding only the numerators 3 and 4 without converting to a common denominator first. Choice C, 33/100, comes from a small addition slip. Choice D, 30/100, is only the converted first fraction and leaves out the second addend entirely.
13. Keisha walked $\frac{1}{10}$ mile and then $\frac{25}{100}$ mile more. Convert: $\frac{1}{10}=\frac{10}{100}$. Add: $\frac{10}{100}+\frac{25}{100}=\frac{35}{100}$. What total distance did she walk?
    Answer: $\frac{35}{100}$ Keisha walked 35/100 mile in total because 1/10 converts to 10/100, and 10/100 + 25/100 = 35/100. Choice B repeats the first distance without adding the second. Choice C adds 1 + 25 = 26 without converting 1/10 to 10/100 first. Choice D is one short of the correct sum.
14. Keisha has $\frac{6}{10}$ of a dollar in dimes and $\frac{7}{100}$ of a dollar in pennies. Convert $\frac{6}{10}$ to hundredths: $\frac{6}{10} = \frac{60}{100}$. Then add: $\frac{60}{100} + \frac{7}{100} = \frac{60+7}{100}$. What fraction of a dollar does she have?
    Answer: $\frac{67}{100}$ This question tests 4th grade ability to express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (CCSS.4.NF.5). To add fractions with denominators 10 and 100, we must first convert to a common denominator—100 is the common denominator since 100 = 10 × 10. The key relationship: 1/10 = 10/100 (one tenth equals ten hundredths), so any fraction a/10 = (10a)/100 by multiplying numerator and denominator by 10. Once both fractions have denominator 100, add the numerators and keep the denominator: (10a)/100 + b/100 = (10a + b)/100. Keisha has 6/10 of a dollar in dimes and 7/100 of a dollar in pennies; convert 6/10 to hundredths: 6/10 = (6 × 10)/100 = 60/100. Then add: 60/100 + 7/100 = (60 + 7)/100 = 67/100. Choice A is correct because converting 6/10: multiply numerator 6 × 10 = 60, denominator 10 × 10 = 100, giving 60/100; then adding: 60/100 + 7/100, add numerators: 60 + 7 = 67, keep denominator 100: 67/100. This demonstrates understanding that tenths must be expressed as hundredths before adding. Choice B represents adding without converting (added 6+7=13 directly), which happens when students don't recognize need for common denominator. To help students: Visualize with hundredths grid (10×10 squares)—each COLUMN is 1/10 = 10 squares, each SQUARE is 1/100. To convert tenths to hundredths, multiply numerator by 10: 6/10 = (6×10)/100 = 60/100. Check: count squares (60 squares for 6 columns). Then add: 60/100 + 7/100 = 67/100 (60 + 7 = 67 squares total). Connect to decimals: 6/10 = 0.6, 7/100 = 0.07, 0.6 + 0.07 = 0.67 = 67/100. Use money: 6 dimes (6/10 dollar) = 60 pennies (60/100 dollar), plus 7 pennies = 67 pennies = 67/100 dollar. Pattern: 1/10=10/100, 2/10=20/100, 6/10=60/100 (multiply numerator by 10). Watch for: not converting tenths to hundredths before adding, multiplying by wrong number, arithmetic errors, and adding denominators.
15. Add: $\frac{3}{10} + \frac{42}{100}$. What is the sum?
    Answer: $\frac{72}{100}$ $\frac{72}{100}$ is correct because $\frac{3}{10} = \frac{30}{100}$, and $\frac{30}{100} + \frac{42}{100} = \frac{72}{100}$. $\frac{45}{100}$ is incorrect because it does not match the correct conversion and sum. $\frac{71}{100}$ is incorrect because it is off by one from the correct sum. $\frac{30}{100}$ is incorrect because it only represents the converted first fraction, not the total.
16. Maya has $\frac{7}{10}$ of a pizza and her brother has $\frac{25}{100}$ of the same size pizza. If they combine their pizza pieces, what fraction of a whole pizza will they have together?
    Answer: $\frac{95}{100}$ First, convert $\frac{7}{10}$ to hundredths: $\frac{7}{10} = \frac{70}{100}$. Then add: $\frac{70}{100} + \frac{25}{100} = \frac{95}{100}$. Choice A incorrectly adds numerators without converting (7 + 25 = 32). Choices C and D incorrectly add denominators (10 + 100 = 110).
17. What is $\frac{2}{10} + \frac{35}{100}$?
    Answer: $\frac{55}{100}$ The correct answer is B, 55/100. Rewriting 2/10 as 20/100 and adding gives 20/100 + 35/100 = 55/100. Choice A, 20/100, is only the converted first fraction, not the final sum. Choice C, 37/100, comes from adding the original numerator 2 to 35 instead of first converting 2/10 to 20/100. Choice D, 65/100, comes from an addition error.
18. What is $\frac{4}{10} + \frac{27}{100}$?
    Answer: $\frac{67}{100}$ Rewrite $\frac{4}{10}$ with denominator 100: $\frac{4}{10} = \frac{40}{100}$. Then add: $\frac{40}{100} + \frac{27}{100} = \frac{67}{100}$. Choice A repeats the converted value of $\frac{4}{10}$ without adding $\frac{27}{100}$. Choice B miscalculates $40+27$. Choice D adds only the original numerators without converting first ($4+27=31$).
19. What is $\frac{3}{10} + \frac{27}{100}$?
    Answer: $\frac{57}{100}$ The correct answer is B, 57/100. Rewriting 3/10 as 30/100 and adding gives 30/100 + 27/100 = 57/100. Choice A, 30/100, is only the converted first fraction, not the final sum. Choice C, 67/100, comes from an addition error. Choice D, 30/1000, comes from converting to the wrong place value.
20. Add: $\frac{3}{10} + \frac{4}{100}$. What is the sum?
    Answer: $\frac{34}{100}$ $\frac{34}{100}$ is correct because $\frac{3}{10} = \frac{30}{100}$, and $\frac{30}{100} + \frac{4}{100} = \frac{34}{100}$. $\frac{30}{100}$ is incorrect because it only represents the converted first fraction. $\frac{33}{100}$ is incorrect because it is off by one from the correct sum. $\frac{7}{100}$ is incorrect because it adds the numerators without converting to a common denominator.

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