1. Calculate. a) $$ \frac{3}{5} \div \frac{1}{3}

Question

1. Calculate. a) $$ \frac{3}{5} \div \frac{1}{3}<5 $$ b) $$ 2 \frac{1}{5}+5 \frac{1}{8} $$ c) $$ 2 \frac{1}{3}+\frac{3}{4} $$ d) $$ \frac{3}{2}+\frac{1}{4}-\frac{1}{3} $$ 2. By how much is $$ 2 \frac{3}{4} $$ more than $$ 1 \frac{5}{6} $$ ? 3. What must be subtracted from $$ 10 \frac{7}{8} $$ to give $$ 4 \frac{1}{4} $$ ? 4. Every month, Ludwe spends $$ \frac{1}{6} $$ of his pocket money on paper, $$ \frac{2}{3} $$ on pencils and $$ \frac{1}{12} $$ on pens. What fraction of his money can he spend every month at the tuckshop?

UpStudy AI · Accepted Answer

Below are the step‐by‐step calculations for each part.

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1. Calculate

a) Evaluate (3/5) ÷ (1/3) and verify it is less than 5.

• Division of fractions means multiplying by the reciprocal:
   (3/5) ÷ (1/3) = (3/5) × (3/1) = 9/5

• Since 9/5 = 1.8 and 1.8 < 5, the answer is 9/5 (which is indeed less than 5).

b) Add 2 1/5 and 5 1/8.

• Convert to improper fractions:
   2 1/5 = (2×5 + 1)/5 = 11/5
   5 1/8 = (5×8 + 1)/8 = 41/8

• Find a common denominator (LCM of 5 and 8 is 40):
   11/5 = (11×8)/40 = 88/40
   41/8 = (41×5)/40 = 205/40

• Add:
   88/40 + 205/40 = 293/40

• As a mixed number, 293 ÷ 40 gives 7 with a remainder of 13:
   293/40 = 7 13/40

c) Add 2 1/3 and 3/4.

• Write 2 1/3 as an improper fraction:
   2 1/3 = (2×3 + 1)/3 = 7/3

• Now add 7/3 and 3/4. Find the common denominator (LCM of 3 and 4 is 12):
   7/3 = (7×4)/12 = 28/12
   3/4 = (3×3)/12 = 9/12

• Sum:
   28/12 + 9/12 = 37/12

• As a mixed number: 37 ÷ 12 is 3 with a remainder of 1:
   37/12 = 3 1/12

d) Compute 3/2 + 1/4 – 1/3.

• Find a common denominator for 2, 4, and 3 (which is 12):
   3/2 = (3×6)/12 = 18/12
   1/4 = (1×3)/12 = 3/12
   1/3 = (1×4)/12 = 4/12

• So,
   18/12 + 3/12 – 4/12 = (18 + 3 – 4)/12 = 17/12

• As a mixed number, 17 ÷ 12 = 1 with a remainder of 5:
   17/12 = 1 5/12

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2. By how much is 2 3/4 more than 1 5/6?

• Convert each to an improper fraction:
  2 3/4 = (2×4 + 3)/4 = 11/4
  1 5/6 = (1×6 + 5)/6 = 11/6

• Subtract the smaller from the larger:
  11/4 – 11/6

• Find a common denominator (LCM of 4 and 6 is 12):
  11/4 = (11×3)/12 = 33/12
  11/6 = (11×2)/12 = 22/12

• Difference:
  33/12 – 22/12 = 11/12

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3. What must be subtracted from 10 7/8 to give 4 1/4?

• Express the numbers as improper fractions:
  10 7/8 = (10×8 + 7)/8 = 87/8
  4 1/4 = (4×4 + 1)/4 = 17/4 = (17×2)/8 = 34/8

• Subtract:
  87/8 – 34/8 = 53/8

• Convert 53/8 to a mixed number: 53 ÷ 8 = 6 with remainder 5,
  so 53/8 = 6 5/8

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4. Every month, Ludwe spends 1/6 of his pocket money on paper, 2/3 on pencils, and 1/12 on pens. What fraction of his money can he spend at the tuckshop?

• First, add the fractions spent:
  1/6 + 2/3 + 1/12

• Write each fraction with a common denominator (the LCM of 6, 3, and 12 is 12):
  1/6 = 2/12
  2/3 = 8/12
  1/12 = 1/12

• Sum:
  2/12 + 8/12 + 1/12 = 11/12

• The remaining fraction for the tuckshop is:
  1 – 11/12 = 1/12

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Final Answers:

1. a) 9/5 (which is less than 5)  
   b) 7 13/40  
   c) 3 1/12  
   d) 1 5/12

2. 2 3/4 is 11/12 more than 1 5/6.

3. 6 5/8 must be subtracted from 10 7/8 to get 4 1/4.

4. Ludwe can spend 1/12 of his money each month at the tuckshop.
1. a) 9/5    b) 7 13/40    c) 3 1/12    d) 1 5/12 2. 2 3/4 is 11/12 more than 1 5/6. 3. 6 5/8 must be subtracted from 10 7/8 to get 4 1/4. 4. Ludwe can spend 1/12 of his money each month at the tuckshop.

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