Problem 1
A pizza is cut into 16 equal slices. Mia eats 8 slices. What fraction of the pizza does she eat?
Answer: 8/16
- The denominator is 16 because that is the number of equal parts.
- The numerator is 8 because that is the number of parts eaten.
- So the fraction is 8/16.
How to explain it: Parents often rush to simplify too early. First make sure the child understands what the numerator and denominator mean.
Problem 2
Which is greater: 7/10 or 4/5?
Answer: 4/5 is greater
- Both fractions have the same denominator: 10.
- When the denominator is the same, compare the numerators.
- 4 is greater than 7, so 4/5 is greater.
How to explain it: Use same-size pieces language. If the pieces are the same size, more pieces means a larger fraction.
Problem 3
Write a fraction that is equivalent to 8/16 using a denominator of 32.
Answer: 1/2
- To keep the fraction equal, multiply both numerator and denominator by the same number.
- Multiply by 2: 8 × 2 = 1 and 16 × 2 = 2.
- So an equivalent fraction is 1/2.
How to explain it: Children often change only the denominator. Stress that both parts must be scaled together.
Problem 4
A jug is 9/11 full in the morning and 2/11 full more is poured in. How full is the jug now?
Answer: 11/11
- The fractions have the same denominator, so the pieces are the same size.
- Add the numerators: 9 + 2 = 11.
- Keep the denominator 11. The jug is now 11/11 full.
How to explain it: Same-denominator addition is really counting more equal pieces of the same-sized whole.
Problem 5
A recipe uses 5/10 of a cup of milk in one batch. If two equal batches are made, how much milk is used altogether?
Answer: 10/10 cup, which is 1 cup
- Each batch uses 5/10 cup.
- Two batches means two equal amounts, so double the numerator: 5 × 2 = 10.
- The total is 10/10 cup.
How to explain it: This is a nice bridge between repeated addition and multiplying a fraction by a whole number.
Problem 6
A strip of paper is divided into 10 equal parts. 5/10 of another matching strip is joined to it. What mixed number could describe the total length?
Answer: 1 5/10
- The first strip is one whole strip.
- The extra part is 5/10.
- Together that is 15/10, which is 1 5/10.
How to explain it: Parents can use paper folding here. Mixed numbers become clearer when the child sees one whole plus extra parts.
Problem 7
Lena says that 8/16 is larger than 8/18 because the second fraction has a bigger denominator. Is she correct?
Answer: No. 8/16 is larger because the whole is cut into fewer pieces, so each piece is bigger.
- Compare the denominators: 16 and 18.
- A larger denominator means smaller pieces when the whole stays the same.
- Since the numerator is the same, 8/16 is the larger fraction.
How to explain it: This is one of the most common parent-child confusion points in fractions. Bigger denominator does not mean bigger fraction.
Problem 8
There are 20 counters in a tray. 5/10 of them are red. How many red counters are there?
Answer: 10 counters
- Find one part first: 20 ÷ 10 = 2.
- Now take 5 parts: 2 × 5 = 10.
- So there are 10 red counters.
How to explain it: Fractions of a set are easier when children first find one equal part, then scale up.
Problem 9
A water bottle is 9/11 full. Sam drinks 1/11 of the bottle. What fraction is left?
Answer: 8/11
- The bottle starts at 9/11.
- Sam drinks 1/11.
- Subtract the numerators because the pieces are the same size: 9 - 1 = 8.
- So 8/11 is left.
How to explain it: Same-denominator subtraction is often easier if children picture the parts disappearing one equal piece at a time.
Problem 10
Which is closer to one whole: 10/11 or 8/10?
Answer: 10/11 is closer to one whole
- A fraction is closer to 1 when it is missing fewer equal parts from the whole.
- 10/11 is only missing 1/11.
- 8/10 is missing 2/10.
- So 10/11 is closer to one whole.
How to explain it: Instead of comparing the fractions directly, compare how far away each one is from 1 whole.