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More Word Problems

More Singapore Math Lessons

The following are some examples of 6th Grade Math Word Problems that deals with ratio and fractions. These word problems are solved with the help of block diagrams or bar models (used in Singapore Math).

**Example:**
Adeline’s salary is of Connie’s salary.

**Fraction of a set word problems**

This video applies multiplying a fraction by a whole number to solve word problems. It uses the Singapore math modeling strategy of a bar model and the "unitary method".

Example:

Sean has 63 classical songs on his mp3 player. That's 7/8 of his entire collection. How many songs does Sean have altogether?**How to solve a problem involving fractions of fractions and fractions of remaining parts?**

Problem:

1/4 of my trail mix recipe is raisins and the rest is nuts. 3/5 of the nuts are peanuts and the rest are almonds. What fraction of my trail mix are almonds?**Model Drawing for 6th Grade**

Examples:

**Fraction Problems**

1. Luke sold 2/7 of his magazines last week and the rest of them this week. If he sold 30 magazines last week, how many magazines did he sell this week?

2. At Fairview Middle School, 3/5 of the 570 students were 6th graders and 2/3 of the remaining students were 7th graders. If the rest were 8th graders, how many 8th graders were there?

3. Kiley had 1200 markers. 2/6 of them were red, 3/6 of them were green, and 1/5 of the remaining amount were blue. The rest of the remaining markers were purple. How many purple markers were there?

**Travel Rate Problems**

4. A hybrid car traveled 360 miles on 6 gallon of gas. How far could that same car travel on 10 gallons of gas?

5. A tugboat traveled 1,200 miles on 60 gallons of gas. How far could this tugboat travel on 90 gallons of gas?

6. A pool is filled with water at the rate of 75 gallons every 6 minutes. How long will it take for the pool to fill with 375 gallons of water?

7. Bathroom tile is placed at a rate of 25 tiles every 5 minutes. How long will it take to place 500 tiles?

More Word Problems

More Singapore Math Lessons

The following are some examples of 6th Grade Math Word Problems that deals with ratio and fractions. These word problems are solved with the help of block diagrams or bar models (used in Singapore Math).

a) Find the ratio of Adeline’s salary to Connie’s salary.

b) Find the ratio of Connie’s salary to Adeline’s salary to their total salary.

* Solution: *

Total number of units = 5 + 2 = 7

From the model, we see that.

a) The ratio of Adeline’s salary to Connie’s salary is 5:2.

b) The ratio of Connie’s salary to Adeline’s salary to their total salary is 2:5:7.

** Example:**
Joanne’s savings is 4 times as much as Pam’s savings.

a) What is the ratio of Joanne’s savings to Pam’s savings to their total savings?

b) What fraction of their total savings is Joanne’s savings?

c) What fraction of Joanne’s savings is Pam’s savings?

d) If both girls save a total of $120, how much does Joanne save?

* Solution:*

a) Total number of units = 5

The ratio of Joanne’s savings to Pam’s savings to their total savings is 4:1:5.

b) The ratio of Joanne’s savings to their total savings is 4:5.

Joanne’s savings is of the total savings.

c) The ratio of Pam’s savings to Joanne’s savings is 1:4.

Pam’s savings is of Joanne’s savings.

d) From the model, we see that

5 units = $120

1 unit = = $24

4 units = 4 × $24 = $96

Joanne saves $96.

This video applies multiplying a fraction by a whole number to solve word problems. It uses the Singapore math modeling strategy of a bar model and the "unitary method".

Example:

Sean has 63 classical songs on his mp3 player. That's 7/8 of his entire collection. How many songs does Sean have altogether?

Problem:

1/4 of my trail mix recipe is raisins and the rest is nuts. 3/5 of the nuts are peanuts and the rest are almonds. What fraction of my trail mix are almonds?

Examples:

1. Luke sold 2/7 of his magazines last week and the rest of them this week. If he sold 30 magazines last week, how many magazines did he sell this week?

2. At Fairview Middle School, 3/5 of the 570 students were 6th graders and 2/3 of the remaining students were 7th graders. If the rest were 8th graders, how many 8th graders were there?

3. Kiley had 1200 markers. 2/6 of them were red, 3/6 of them were green, and 1/5 of the remaining amount were blue. The rest of the remaining markers were purple. How many purple markers were there?

4. A hybrid car traveled 360 miles on 6 gallon of gas. How far could that same car travel on 10 gallons of gas?

5. A tugboat traveled 1,200 miles on 60 gallons of gas. How far could this tugboat travel on 90 gallons of gas?

6. A pool is filled with water at the rate of 75 gallons every 6 minutes. How long will it take for the pool to fill with 375 gallons of water?

7. Bathroom tile is placed at a rate of 25 tiles every 5 minutes. How long will it take to place 500 tiles?

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