The following are some examples of 5th Grade Math Word Problems that deals with ratio and proportions. The word problems are solved with the help of block diagrams or bar models (used in Singapore Math). Block diagrams are also called tape diagrams in the Common Core Math.

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More Word Problems

**Example:**

A zoo has 96 chickens and ducks altogether. The ratio of the number of chickens to the number of ducks is 5:3. How many chickens does the zoo have?

*Solution: *

#### Singapore Math 1 (a Grade 5 problem from a Singapore text)

This video compares the methods of solving a problem taken from a Singapore 5th grade text. It's solved algebraically (US method) and then visually (Singapore method). Viewers are asked to decide which one they like better and why?

Example: Jeremy bought 8 identical pens and 5 identical notebooks. Each notebook costs 30 vents more than each pen. How much did Jeremy spend altogether?**Examples of solving some basic ratio word problems**

Examples:

1. A board was cut into two pieces whose lengths are in the ratio 2:5. The longest piece was 85 inches. How long was the shortest piece?

2. At a track meet, 5/8 of the students were boys. There were 48 more boys. How many students were there altogether?

3. Theresa read two and one-fourth times as many pages on Saturday as on Sunday. She read 120 pages more on Saturday. How many pages did she read altogether?**Solutions to some more involved ratio word problems**

Examples:

1. The ratio of pigs to cows to sheep on the farm is 2:4:7. There are 65 more sheep than pigs. How many cows are there on the farm?

2. Archimedes, Hypatia and Zeno shared a sum of money.Archimedes received 1/6 of the money. Hypatia and Zeno shared the rest of the money in the ratio 2:3. Zeno got $7 more than Hypatia. How much money did they share altogether?

3. One-third of Elmer's age is the same as two-fifths of Sam's age.

a) Draw a bar model representing the situation

b) Elmer is 5 years older than Sam. How old is Sam?

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More Word Problems

A zoo has 96 chickens and ducks altogether. The ratio of the number of chickens to the number of ducks is 5:3. How many chickens does the zoo have?

Total number of units = 5 + 3 = 8

8 units → 96

1 unit → 96 ÷ 8 = 12

5 units → 5 × 12 = 60

The zoo has 60 chickens.*Example:*

Charlie divides a basket of cherries into two portions. The ratio of the mass of the bigger portion to the mass of the smaller portion is 5: 2. If the mass of the bigger portion is 15 kg, find the mass of the smaller portion.

* Solution:*

5 units → 15 kg

1 unit → 15 ÷ 5 = 3 kg

2 units → 2 × 3 = 6 kg

The mass of the smaller portion of cherries is 6 kg.Example: Jeremy bought 8 identical pens and 5 identical notebooks. Each notebook costs 30 vents more than each pen. How much did Jeremy spend altogether?

Examples:

1. A board was cut into two pieces whose lengths are in the ratio 2:5. The longest piece was 85 inches. How long was the shortest piece?

2. At a track meet, 5/8 of the students were boys. There were 48 more boys. How many students were there altogether?

3. Theresa read two and one-fourth times as many pages on Saturday as on Sunday. She read 120 pages more on Saturday. How many pages did she read altogether?

Examples:

1. The ratio of pigs to cows to sheep on the farm is 2:4:7. There are 65 more sheep than pigs. How many cows are there on the farm?

2. Archimedes, Hypatia and Zeno shared a sum of money.Archimedes received 1/6 of the money. Hypatia and Zeno shared the rest of the money in the ratio 2:3. Zeno got $7 more than Hypatia. How much money did they share altogether?

3. One-third of Elmer's age is the same as two-fifths of Sam's age.

a) Draw a bar model representing the situation

b) Elmer is 5 years older than Sam. How old is Sam?

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