Grade 7 Operations on Rational Numbers

Step 1: Identify the rational numbers being added: 3/7 and 2/7.

Step 2: Check the denominators. They are the same (both are 7).

Step 3: When denominators are the same, add the numerators directly.

Numerator sum = 3 + 2 = 5.

Step 4: Keep the common denominator.

The denominator is 7.

Result: The sum is 57.

So, 37 + 27 = 57.

Step 1: Identify the rational numbers: 1/2 and 1/3.

Step 2: Find the Least Common Multiple (LCM) of the denominators (2 and 3).

LCM(2, 3) = 6.

Step 3: Convert each fraction into an equivalent fraction with the LCM as the new denominator.

• For 1/2: Multiply numerator and denominator by 3 (since 2 x 3 = 6). 12 = 1 x 32 x 3 = 36.
• For 1/3: Multiply numerator and denominator by 2 (since 3 x 2 = 6). 13 = 1 x 23 x 2 = 26.

Step 4: Now that the denominators are the same, add the new numerators.

Numerator sum = 3 + 2 = 5.

Step 5: Keep the common denominator (6).

Result: The sum is 56.

So, 12 + 13 = 56.

Step 1: Identify the rational numbers: 5/8 and 1/4.

Step 2: Find the LCM of the denominators (8 and 4).

LCM(8, 4) = 8.

Step 3: Convert each fraction to an equivalent fraction with the LCM as the new denominator.

• For 5/8: The denominator is already 8. 58 remains 58.
• For 1/4: Multiply numerator and denominator by 2 (since 4 x 2 = 8). 14 = 1 x 24 x 2 = 28.

Step 4: Subtract the new numerators.

Numerator difference = 5 - 2 = 3.

Step 5: Keep the common denominator (8).

Result: The difference is 38.

So, 58 - 14 = 38.

Step 1: Identify the rational numbers being multiplied: 2/3 and 4/5.

Step 2: Multiply the numerators together.

Numerator product = 2 x 4 = 8.

Step 3: Multiply the denominators together.

Denominator product = 3 x 5 = 15.

Step 4: Write the product as a new fraction with the numerator product over the denominator product.

The product is 815.

Step 5: Simplify the resulting fraction if possible (in this case, it's already in simplest form).

So, 23 x 45 = 815.

Step 1: Identify the rational numbers: 1/2 (dividend) and 1/4 (divisor).

Step 2: Division by a fraction is the same as multiplication by its reciprocal. Find the reciprocal of the divisor (1/4).

The reciprocal of 14 is 41 (or simply 4).

Step 3: Change the division problem to a multiplication problem using the reciprocal.

12 ÷ 14 becomes 12 x 41.

Step 4: Multiply the fractions (numerator by numerator, denominator by denominator).

Numerator product = 1 x 4 = 4.

Denominator product = 2 x 1 = 2.

The product is 42.

Step 5: Simplify the resulting fraction.

42 can be simplified by dividing both numerator and denominator by their HCF, which is 2.

4 ÷ 22 ÷ 2 = 21 (or simply 2).

Result: The quotient is 2.

So, 12 ÷ 14 = 2.