Stabroek News Sunday

# 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: