The following are some examples of 6th Grade Math Word Problems that deals with ratio and proportions. The word problems are solved with the help of tape diagrams, block diagrams or bar model (Singapore Math)

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More Singapore Math Word Problems

**Example:**

Mark and Fred had some money in the ratio 6:1. Mark gave half of his money to Fred. Find the ratio of the amount of money Mark had left to the amount of money Fred had in the end.

**Solution:**

**Before**

**After**

The ratio of the amount of money Mark had left to the amount of money Fred had in the end is 3:4.

**Example:**

Carol puts some green and red unit cubes in a box. The ratio of the number of green cubes to the number of red cubes is 2:1. She adds 12 more red cubes in the box and the ratio becomes 4:5.

a) How many green cubes are there in the box?

b) How many red cubes does Carol have in the end?

**Solution:**

**Before**

**After**

From the model, we see that:

a) 3 units = 12 cubes

1 unit = 12 ÷3 = 4 cubes

4 units = 4 × 4 = 16 cubes

There are 16 green cubes in the box.

b) 5 units = 5 × 4 = 20 cubes

Carol has 20 red cubes in the end.

**How to solve ratio word problems?**

Examples:

- 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?

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

- 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?

**How to solve more difficult ratio word problems?**

Examples:

- 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?

- 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?

- 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?

**How to use proportions to solve ratio problems?**

- At Al’s Catering Service, they often make a large batch of fruit salad. The ratio of cups of apples to cups of oranges in the recipe is 8 : 5.

a) If they use 15 cups of oranges, how many cups of apples should they use?

b) If they only use 2 cups of apples, how many cups of oranges should they use?

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