Operations and Measurements with Weight in Kilograms and Grams for Primary 4

Weight

Performance Objectives

By the end of the lesson, students should be able to:

1. compute addition and subtraction of weights using kg and g;
2. multiply and divide weights by whole numbers.

What is Weight?

Weight is a measure of how heavy an object is.

When you lift a bag of rice or a bucket of water, you feel how heavy it is. This heaviness is its weight. Different objects have different weights.

Units of Weight: Kilograms and Grams

In Nigeria, we commonly measure weight using two main units: kilograms and grams.

Kilograms (kg)

Kilograms are used to measure heavier objects. For example, the weight of a person, a bag of cement, or a large sack of garri is measured in kilograms.

The short form for kilogram is kg.

Grams (g)

Grams are used to measure lighter objects. For example, the weight of a small sachet of sugar, a pencil, or a few grains of rice is measured in grams.

The short form for gram is g.

Relationship Between Kilograms and Grams

Kilograms and grams are related. One kilogram is equal to one thousand grams.

$$1 \text{ kg} = 1000 \text{ g}$$

This relationship is important when you need to convert between kilograms and grams, especially during calculations.

Measuring Weight

We use special tools to measure weight accurately. Common tools for measuring weight include:

1. Weighing Scale: This is a common tool used in homes, markets, and clinics to measure the weight of people or goods.
2. Scale Balance: This tool compares the weight of an unknown object with known standard weights to find its measure.

Observe the images below showing common weighing tools.

Operations with Weights

Just like with ordinary numbers, we can add, subtract, multiply, and divide weights. When performing these operations, it is important to keep kilograms and grams separate and remember their relationship.

Adding Weights in Kilograms and Grams

To add weights, you add the grams together and the kilograms together. If the sum of grams is 1000 or more, you convert 1000 grams into 1 kilogram and add it to the kilogram column.

The steps for adding weights are:

1. Write the weights in columns, with kilograms under kilograms and grams under grams.
2. Add the grams column first.
3. If the sum of grams is 1000 or more, divide it by 1000 to get kilograms and remaining grams. Write down the remaining grams and carry over the kilograms to the kilogram column.
4. Add the kilograms column, including any carried-over kilograms.

Example 1: Add 5 kg 300 g and 3 kg 450 g.

$$
\begin{array}{r}
\text{kg} \quad \text{g} \\
5 \quad 300 \\
+3 \quad 450 \\
\hline
8 \quad 750
\end{array}
$$

Answer: 8 kg 750 g

Example 2: Add 7 kg 800 g and 4 kg 500 g.

First, add the grams:

$$800 \text{ g} + 500 \text{ g} = 1300 \text{ g}$$

Convert 1300 g to kg and g:

$$1300 \text{ g} = 1 \text{ kg } 300 \text{ g}$$

Write down 300 g and carry over 1 kg to the kilogram column.

Next, add the kilograms:

$$7 \text{ kg} + 4 \text{ kg} + 1 \text{ kg (carried over)} = 12 \text{ kg}$$

So, the sum is:

$$
\begin{array}{r}
\text{kg} \quad \text{g} \\
\overset{1}{7} \quad 800 \\
+4 \quad 500 \\
\hline
12 \quad 300
\end{array}
$$

Answer: 12 kg 300 g

Subtracting Weights in Kilograms and Grams

To subtract weights, you subtract the grams from grams and kilograms from kilograms. If you need to subtract a larger number of grams from a smaller number of grams, you “borrow” 1 kilogram from the kilogram column and convert it to 1000 grams.

The steps for subtracting weights are:

1. Write the weights in columns, with kilograms under kilograms and grams under grams.
2. Subtract the grams column first.
3. If the grams in the top number are smaller than the grams in the bottom number, borrow 1 kg from the kilogram column. Convert the borrowed 1 kg to 1000 g and add it to the grams in the top number. Then subtract.
4. Subtract the kilograms column, remembering to reduce the kilogram in the top number if you borrowed from it.

Example 1: Subtract 2 kg 150 g from 6 kg 300 g.

$$
\begin{array}{r}
\text{kg} \quad \text{g} \\
6 \quad 300 \\
-2 \quad 150 \\
\hline
4 \quad 150
\end{array}
$$

Answer: 4 kg 150 g

Example 2: Subtract 3 kg 700 g from 9 kg 200 g.

First, look at the grams column. We cannot subtract 700 g from 200 g. So, we borrow 1 kg from the 9 kg, leaving 8 kg.

Convert the borrowed 1 kg to 1000 g and add it to the 200 g:

$$1000 \text{ g} + 200 \text{ g} = 1200 \text{ g}$$

Now, subtract the grams:

$$1200 \text{ g} – 700 \text{ g} = 500 \text{ g}$$

Next, subtract the kilograms:

$$8 \text{ kg} – 3 \text{ kg} = 5 \text{ kg}$$

So, the difference is:

$$
\begin{array}{r}
\text{kg} \quad \text{g} \\
\overset{8}{9} \quad \overset{1200}{200} \\
-3 \quad 700 \\
\hline
5 \quad 500
\end{array}
$$

Answer: 5 kg 500 g

Multiplying Weights by Whole Numbers

To multiply a weight by a whole number, you multiply the grams by the number and the kilograms by the number separately. If the product of grams is 1000 or more, convert it to kilograms and grams and add the kilograms to the kilogram product.

The steps for multiplying weights are:

1. Multiply the grams by the whole number.
2. If the product of grams is 1000 or more, divide it by 1000 to get kilograms and remaining grams. Write down the remaining grams and carry over the kilograms.
3. Multiply the kilograms by the whole number, and then add any carried-over kilograms.

Example 1: Multiply 4 kg 120 g by 3.

First, multiply the grams:

$$120 \text{ g} \times 3 = 360 \text{ g}$$

Next, multiply the kilograms:

$$4 \text{ kg} \times 3 = 12 \text{ kg}$$

So, the product is:

$$
\begin{array}{r}
\text{kg} \quad \text{g} \\
4 \quad 120 \\
\times \quad \quad 3 \\
\hline
12 \quad 360
\end{array}
$$

Answer: 12 kg 360 g

Example 2: Multiply 2 kg 600 g by 4.

First, multiply the grams:

$$600 \text{ g} \times 4 = 2400 \text{ g}$$

Convert 2400 g to kg and g:

$$2400 \text{ g} = 2 \text{ kg } 400 \text{ g}$$

Write down 400 g and carry over 2 kg to the kilogram column.

Next, multiply the kilograms and add the carried-over kilograms:

$$2 \text{ kg} \times 4 = 8 \text{ kg}$$
$$8 \text{ kg} + 2 \text{ kg (carried over)} = 10 \text{ kg}$$

So, the product is:

$$
\begin{array}{r}
\text{kg} \quad \text{g} \\
\overset{2}{2} \quad 600 \\
\times \quad \quad 4 \\
\hline
10 \quad 400
\end{array}
$$

Answer: 10 kg 400 g

Dividing Weights by Whole Numbers

To divide a weight by a whole number, you divide the kilograms first. Any remainder in kilograms is converted to grams and added to the existing grams. Then, the total grams are divided by the whole number.

The steps for dividing weights are:

1. Divide the kilograms by the whole number. Write down the quotient.
2. If there is a remainder in kilograms, convert it to grams by multiplying by 1000.
3. Add these converted grams to the grams already present in the weight.
4. Divide the total grams by the whole number. Write down the quotient.

Example 1: Divide 9 kg 600 g by 3.

First, divide the kilograms:

$$9 \text{ kg} \div 3 = 3 \text{ kg}$$

Next, divide the grams:

$$600 \text{ g} \div 3 = 200 \text{ g}$$

So, the result is:

$$
\begin{array}{r}
3 \text{ kg} \quad 200 \text{ g} \\
3 \overline{\smash{)} 9 \text{ kg} \quad 600 \text{ g}}
\end{array}
$$

Answer: 3 kg 200 g

Example 2: Divide 7 kg 500 g by 5.

First, divide the kilograms:

$$7 \text{ kg} \div 5 = 1 \text{ kg} \text{ with a remainder of } 2 \text{ kg}$$

Convert the remainder 2 kg to grams:

$$2 \text{ kg} = 2 \times 1000 \text{ g} = 2000 \text{ g}$$

Add these 2000 g to the existing 500 g:

$$2000 \text{ g} + 500 \text{ g} = 2500 \text{ g}$$

Next, divide the total grams:

$$2500 \text{ g} \div 5 = 500 \text{ g}$$

So, the result is:

$$
\begin{array}{r}
1 \text{ kg} \quad 500 \text{ g} \\
5 \overline{\smash{)} 7 \text{ kg} \quad 500 \text{ g}} \\
\quad \underline{-5 \text{ kg}} \\
\quad 2 \text{ kg} \quad \rightarrow 2000 \text{ g} \\
\quad \quad \quad \quad +500 \text{ g} \\
\quad \quad \quad \quad 2500 \text{ g} \\
\quad \quad \quad \quad \underline{-2500 \text{ g}} \\
\quad \quad \quad \quad \quad 0 \text{ g}
\end{array}
$$

Answer: 1 kg 500 g