Problem Set 15 – Making Pairs and Dividing by Two-Digit NumbersClass 5 Maths · Chapter 4 Multiplication and Division · Problem Set 15 – Maharashtra Board

Summary: Problem Set 15 – Making Pairs and Dividing by Two-Digit Numbers

If one group has 4 things and another has 3, picking one from each gives 4 × 3 = 12 different pairs.

Every multiplication gives two divisions: from 8 × 6 = 48 we get 48 ÷ 6 = 8 and 48 ÷ 8 = 6.

Long division goes from the left: divide, multiply, subtract, bring down the next digit — and repeat.

If the divisor does not fit into a part, write 0 in the quotient for that place. To guess a digit, compare the first digits, then test it.

Check: divisor × quotient + remainder = dividend. The remainder must always be smaller than the divisor.

Key points to remember

• Number of pairs = objects in group 1 × objects in group 2
• Dividend ÷ divisor = quotient, with a remainder
• Steps: divide, multiply, subtract, bring down
• Write 0 in the quotient when the divisor does not fit
• Guess the quotient digit from the first digits, then test
• Remainder < divisor, always
• Check: divisor × quotient + remainder = dividend
• Distance ÷ speed = time; total ÷ price of one = how many

Problem Set 15 – Making Pairs and Dividing by Two-Digit Numbers – Notes

1. Pairing off objects from two groups

• Riya has 4 caps and 3 scarves. She wears one cap and one scarf.
• Each cap can go with each of the 3 scarves, so there are 3 + 3 + 3 + 3 = 4 × 3 = 12 pairs.
• Rule: the number of different pairs is the product of the sizes of the two groups.

2. Division by a one-digit number (a reminder)

• Split the number into easy parts: 432 ÷ 6 → 420 ÷ 6 = 70 and 12 ÷ 6 = 2, so the quotient is 72.
• If the first digit is smaller than the divisor, take the first two digits together.
• If a digit in the middle is too small to share, write 0 in the quotient there.

3. Long division by a two-digit number

• Start with as many left digits as you need to make a number at least as big as the divisor.
• Guess the next quotient digit by dividing the first digit(s) of that number by the first digit of the divisor.
• Multiply the guess by the divisor. If it is too big, try one less; if the leftover is bigger than the divisor, try one more.

4. Checking a division

• Multiply the divisor by the quotient and add the remainder.
• The result must equal the dividend.
• Also make sure the remainder is less than the divisor — otherwise the quotient digit was too small.

5. Word problems with division

• Equal sharing: 1625 books packed equally in 25 boxes → 1625 ÷ 25 = 65 books per box.
• Speed: 455 km at 65 km per hour takes 455 ÷ 65 = 7 hours.
• 'Which number × 47 gives 8366?' → divide: 8366 ÷ 47 = 178.
• 'How many at the most, and how many left?' → the quotient is how many, the remainder is what is left.

Formulas at a glance

Key terms

Problem Set 15 – Making Pairs and Dividing by Two-Digit Numbers – Flashcards

Read the question, answer it in your head, then tap the card to check. 10 cards.

Problem Set 15 – Making Pairs and Dividing by Two-Digit Numbers – MCQ Quiz

10 questions. Tap an option — you will see at once if it is right and why.

How to study Problem Set 15 – Making Pairs and Dividing by Two-Digit Numbers

⏱ About 35 minutes

1. Pairs (5 min)
   Draw 4 caps and 3 scarves and join every cap to every scarf. Count the lines: 12.
2. Divide (20 min)
   Redo 7618 ÷ 34 on paper, then the 4 'Try it yourself' sums.
3. Check (10 min)
   Check each division by multiplying back, then take the quiz and play 🎮 Play.