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Std 5 Mathematics · Chapter 16

16. Preparation for Algebra

Solutions to Problem Sets 54 to 56 — expressions, equalities, inequalities and using letters for numbers. Maharashtra State Board (Balbharati), Grade Five Mathematics, Part Two.

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Key Ideas

Expression: numbers joined by an operation and written in brackets, such as (6 + 6), (15 − 3), (6 × 2), (24 ÷ 2).
Equality: two expressions with the same value joined by “=”, for example (6 + 6) = (15 − 3).
Inequality: two expressions with different values, shown by ≠, < or >, for example (9 − 5) < (15 ÷ 3).
Letters for numbers: a letter such as a can stand for any number, so a rule can be written in short: (a + b) = (b + a), a × 1 = a.

Problem Set 54

1Using brackets, write three pairs of numbers whose sum is 13. Use them to write three equalities.

Three pairs: (6 + 7), (9 + 4), (10 + 3). The value of each is 13.

Equalities:

  1. (6 + 7) = (9 + 4)
  2. (9 + 4) = (10 + 3)
  3. (6 + 7) = (10 + 3)

Other pairs such as (8 + 5), (11 + 2) or (12 + 1) are also correct, as long as each sum is 13.

2Find four pairs of numbers, one for each of addition, subtraction, multiplication and division that make the number 18. Write the equalities for each of them.
  • Addition: (10 + 8) = 18
  • Subtraction: (20 − 2) = 18
  • Multiplication: (6 × 3) = 18
  • Division: (36 ÷ 2) = 18

Equalities between them:

  1. (10 + 8) = (20 − 2)
  2. (6 × 3) = (36 ÷ 2)
  3. (10 + 8) = (6 × 3)
  4. (20 − 2) = (36 ÷ 2)

Other correct choices include (9 + 9), (25 − 7), (9 × 2) and (54 ÷ 3).

Problem Set 55

1Say whether right or wrong.
  1. (23 + 4) = (4 + 23) — Right (27 = 27)
  2. (9 + 4) > 12 — Right (13 > 12)
  3. (9 + 4) < 12 — Wrong (13 is not less than 12)
  4. 138 > 138 — Wrong (a number cannot be greater than itself)
  5. 138 < 138 — Wrong (a number cannot be less than itself)
  6. 138 = 138 — Right
  7. (4 × 7) = 30 − 2 — Right (28 = 28)
  8. 255 > 5 — Wrong (255 = 5, and 5 is not greater than 5)
  9. (5 × 8) = (8 × 5) — Right (40 = 40)
  10. (16 + 0) = 0 — Wrong (16 + 0 = 16, not 0)
  11. (16 + 0) = 16 — Right (16 = 16)
  12. (9 + 4) = 12 — Wrong (13 ≠ 12)
2Fill in the blanks with the right symbol from <, > or =.
  1. (45 ÷ 9) = (9 − 4) (5 = 5)
  2. (6 + 1) > (3 × 2) (7 > 6)
  3. (12 × 2) < (25 + 10) (24 < 35)

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3Fill in the blanks in the expressions with the proper numbers.
  1. (1 × 7) = (7 × 1) — 1 × 7 = 7, and 7 × 1 = 7
  2. (5 × 4) > (7 × 2) — 20 > 14. Any of 0, 1 or 2 is correct, since 7 × 3 = 21 is too big.
  3. (48 ÷ 3) < (4 × 5) — 16 < 20. Any number 4 or more is correct, since 3 × 5 = 15 is too small.
  4. (0 + 1) > (5 × 0) — 1 > 0. Only 0 works, since 5 × 1 = 5 is already more than 1.
  5. (35 ÷ 7) = (2 + 3) — 5 = 5. Also correct: 1 + 4, 0 + 5 and so on.
  6. (6 − 2) < (2 + 3) — 4 < 5. Any of 2, 3, 4, 5 or 6 is correct, since 6 − 1 = 5 is not less than 5.

As the textbook explains, when a statement has several correct answers, writing any one of them is enough.

Using Letters

ATake the value of a as 8 and b as 4 and verify that (a ÷ b) ≠ (b ÷ a).

a ÷ b = 8 ÷ 4 = 2, but b ÷ a = 4 ÷ 8 = 12. Since 2 ≠ 12, the property (a ÷ b) ≠ (b ÷ a) is verified.

Problem Set 56

1Use a letter for ‘any number’ and write the following properties in short.
  1. The sum of any number and zero is the number itself: a + 0 = a
  2. The product of any two numbers and the product obtained after changing the order of those numbers is the same: a × b = b × a
  3. The product of any number and zero is zero: a × 0 = 0

Any letters may be used, for example x + 0 = x or p × q = q × p.

2Write the following properties in words.
  1. m − 0 = m: When zero is subtracted from any number, the answer is the number itself.
  2. n ÷ 1 = n: When any number is divided by 1, the answer is the number itself.
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