# Grade Five Mathematics

## Answers to last week’s questions

Exercise 1 1. 3/4 2. 1/6 3. 1/3 4. 7/8 5. 5/6

Exercise 2

1. Proper fraction 2. Improper fraction 3. Mixed number 4. Improper fraction 5. Proper fraction 6. Proper fraction 7. Mixed fraction 8. Improper Fraction

Exercise 3 a. 2 3/4 b. 2 2/5 c. 3 1/2 d. 1 7/9 e. 1 3/9 f. 37/4 g. 23/4 h. 14/5 i. 68/9 j. 28/11 k. 49/10

Greetings, students. How are you, today? I trust that you are doing well. Last week we started a new topic, where we looked at the general concept of fractions. Today, we will continue to look at fractions, however, we will specifically examine the concept of addition and subtraction of same.

In our last session, we learned that a fraction is part of a whole.

Boys and girls, I’m confident you know how to add and subtract whole numbers, but did you know we can also add and subtract fractions? Let’s discover how:

Addition of fractions with a common denominator

Simply put; if denominators of two or more fractions are the same, then we can directly add the numerators, keeping the denominator common.

For example: Calculate:

Since the denominators are the same, therefore we can add the numerators directly.

When we simplify the fraction, we get:

Hence, the sum of and is 2.

It’s that simple! I hope you understand. If not, carefully examine the example once more.

Now students, let’s continue to look at addition of fractions, but this time with unlike denominators (denominators that are not the same).

Adding fractions with different Denominators

Rule- When two or more fractions with different denominators are added together, then we cannot add the numerators directly.

We must make the denominators of the fractions the same, by finding the Lowest Common Multiple (LCM) of the denominators and rationalizing them.

N.B: The L.C.M is the smallest positive number that is a multiple of two or more numbers.

For example: 3 + 1 4 6

Step 1- Find the lowest common multiple of both denominators. The LCM of 4 & 6 is 12.

Step 2 - Rename each fraction. Multiply the denominator by a number that will give you the L.C.M (12). Multiply the numerator by the same number. (In this example, we’ll multiply the denominator and numerator of the first fraction by 3, and the denominator and numerator of the second fraction by 2).

3x3 + 1x2 4x3 6x2

= 9 + 12

2 12

Step 3 Add both numerators and write back the whole (denominator)

9+ 2 = 12

Now that we know how to add fractions with like and unlike denominators, let’s work the following.

Exercise 1

Find the sum of the following fractions:

Excellent work, boys and girls! Let’s now examine the concept of subtraction of fractions:

Subtraction of Fractions

There are 3 simple steps to subtract fractions

● Step 1. Make sure the denominators are the same (if not, as we did with the addition of fractions, we find the L.C.M in order to derive a common denominator).

● Step 2. Subtract the numerators. Put the answer over the same

denominator.

● Step 3. Simplify the fraction (if needed).

For example:

L.C.M of 15 and 6 = 30

Multiply the denominator by a number that will give you the L.C.M (30). Multiply the numerator by the same number.

=6x2 –2x5 15 x 2 6 x 5

12 - 10 30

= 2 30

## 11 12

= when simplified = 1 15

Let’s practice working a few:

## Exercise 2

Subtract the following fractions and simplify your answers to their simplest form: