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A fraction is a part of a whole number. As an example, you can have one whole pizza. If you cut the pizza in half (a fraction), you will now have two halves. Two halves equal one whole. Below is a series of ten fraction questions. Can you get the correct fraction for each one?

1.

4/10 + 5/8 = ?

4/10 + 5/8 = 20/18 = 1 ^{2}⁄_{18} = 1 ^{1}⁄_{9}

4/10 + 5/8 = 9/18 = 1/2

4/10 + 5/8 = 16/40 + 25/40 = 41/40 = 1 ^{1}⁄_{40}

4/10 + 5/8 = 4/40 + 5/40 = 9/40

2.

5/8 + 1/8 = 6/8 = ?

2/3

2/4

1/2

3/4

6/8 can be simplified by dividing 6 by 2 = 3 and dividing 8 by 2 = 4 giving you 3/4

3.

What is the equivalent fraction of 18/30?

6/10

9/15

3/5

2/3

The problem is solved as: 18/30 divided by 2 = 9/15; 18/30 divided by 3 = 6/10; 18/30 divided by 6 = 3/5

4.

How would you write a fraction to show one whole square that is divided by nine equal squares? Three of the nine squares are blue. Two of the nine squares are red. Two of the nine squares are yellow. One of the nine squares is green and one is brown.

3/9 + 2/9 + 2/9 + 1/9 + 1/9 = 9/9 = 1

3/3 + 3/3 + 3/3 = 9/3 = 3

1 ÷ 9/9 = 1 ÷ 1 = 0

9/3 x 1 = 9/3 x 1/1 = 9/3 = 3

We know that we have nine equal squares, three of which are blue so we get 3/9. Two squares are red so we have 2/9. Two squares are yellow so we have another 2/9. One square is green so we have 1/9 and one square is brown so we have another 1/9. The common denominator is 9 so we add the numerators: 3 + 2 + 2 + 1 + 1 = 9. This gives us 9/9 which equal 1 whole square

5.

9/12 x 11 = ?

1 ^{2}⁄_{3}

99

8 ^{1}⁄_{4}

10

To multiply fractions you need to multiply the numerators with each other. You then need to multiply the denominators with each other. When you have a whole number as we have here, i.e., 11, the denominator is always the number 1. So our problem would look like 9/12 x 11/1. You next multiply the numerators 9 x 11 = 99. You then multiply the denominators 12 x 1 = 12. This gives you 99/12. You need to reduce that fraction down by dividing the numerator by the denominator so 99 is divided by 12 giving you the whole number 8 and leaving you with 3/12. 8 3/12 can be reduced downward as both 3 and 12 can be divided by 3 giving you 1/4. The problem is solved as: 9/12 x 11/1 = 99/12 = 8 ^{3}⁄_{12} = 8 ^{1}⁄_{4}

6.

3/16 + 7/16 = ? = ?

10/16 = 5/8

10/16 = 1 ^{1}⁄_{4}

21/16 = 1 ^{5}⁄_{16}

10/8 = 1 ^{1}⁄_{4}

Add the numerators 3 + 7 = 10. We have a common denominator of 16 so we get 10/16. We can then simplify 10/16 by dividing by 2 (10 divided by 2 = 5; 16 divided by 2 = 8) and getting 5/8

7.

3 x 2/6 = ?

5/6

6/7

1 ^{1}⁄_{7}

1

As you are multiplying in this fraction, you will need to multiply the numerators with each other and you need to multiply the denominators with each other. When you have a whole number as we have here, i.e., 3, the denominator is always the number 1. So our problem would look like 3/1 x 2/6. You next multiply the numerators 3 x 2 = 6 and then you multiply the denominators 1 x 6 = 6. This gives you 6/6. You need to reduce that down by dividing the numerator by the denominator so 6 is divided by 6 giving you a whole number 1. The problem is solved as: 3/1 x 2/6 = 6/6 = 1

8.

For the fractions 1/2, 3/8 and 9/14, which numbers are the denominators?

1/2

1, 3, 9

2, 8, 14

3/8 and 8/14

The denominator is the bottom number in a fraction

9.

5 x 3/5 = ?

15

3

5

20

When multiplying fractions you multiply the numerators with each other and you multiply the denominators with each other. When you have a whole number as we have here, i.e., 5, the denominator is always the number 1. So our problem would look like 5/1 x 3/5. You next multiply the numerators 5 x 3 = 15 and then you multiply the denominators 1 x 5 = 5. This gives you 15/5. You need to reduce that down by dividing the numerator by the denominator so 15 is divided by 5 giving you a whole number 3. The problem is solved as: 5/1 x 3/5 = 15/5 = 3

10.

For the fractions 3/4, 7/10 and 6/15, which numbers are the numerators?

4, 10, 15

3, 7, 6

10

6

The numerator is the top number in a fraction

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40. To find the common denominator we must find a number to multiple each denominator to get to the number 40. To get 10 to 40 we need to multiply it by 4. To get 8 to 40 we need to multiply it by 5. (10 x 4 = 40 and 8 x 5 = 40) Since we multiplied the denominators we must also multiply the numerators by the same numbers. This gives us 4 x 4 = 16 and 5 x 5 = 25. Our fractions will now look like this: 16/40 + 25/40. Now we need to add the numerators 16 + 25 = 41 giving us 41/40. We can reduce that fraction down to get 1^{1}⁄_{40}