Askiitians Tutor Team
Last Activity: 26 Days ago
Let's solve both parts step by step, simplifying using appropriate properties of fractions and arithmetic.
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### Part (i):
Expression:
`- (2/3) × (3/5) + (5/2) - (3/5) × (1/6)`
**Step 1: Simplify each term**
1. `- (2/3) × (3/5)`
Multiply the numerators and the denominators:
`= -(2 × 3) / (3 × 5)`
`= -6 / 15`
Simplify: `-6/15 = -2/5`.
2. `(3/5) × (1/6)`
Multiply the numerators and the denominators:
`= (3 × 1) / (5 × 6)`
`= 3 / 30`
Simplify: `3/30 = 1/10`.
**Step 2: Substitute back into the expression**
The expression becomes:
`- 2/5 + 5/2 - 1/10`.
**Step 3: Find a common denominator**
The denominators are `5`, `2`, and `10`. The least common denominator (LCD) is `10`.
Convert all terms:
`-2/5 = -4/10`
`5/2 = 25/10`
`-1/10` stays the same.
**Step 4: Combine the terms**
`-4/10 + 25/10 - 1/10 = ( -4 + 25 - 1 ) / 10`
`= 20/10`.
**Step 5: Simplify the result**
`20/10 = 2`.
**Final Answer for (i):** `2`.
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### Part (ii):
Expression:
`(2/5) × (-3/7) - (1/6) × (3/2) + (1/14) × (2/5)`
**Step 1: Simplify each term**
1. `(2/5) × (-3/7)`
Multiply the numerators and the denominators:
`= (2 × -3) / (5 × 7)`
`= -6 / 35`.
2. `(1/6) × (3/2)`
Multiply the numerators and the denominators:
`= (1 × 3) / (6 × 2)`
`= 3 / 12`
Simplify: `3/12 = 1/4`.
3. `(1/14) × (2/5)`
Multiply the numerators and the denominators:
`= (1 × 2) / (14 × 5)`
`= 2 / 70`
Simplify: `2/70 = 1/35`.
**Step 2: Substitute back into the expression**
The expression becomes:
`-6/35 - 1/4 + 1/35`.
**Step 3: Combine like terms**
For `-6/35 + 1/35`, combine the fractions with the same denominator:
`= (-6 + 1) / 35`
`= -5/35`.
Simplify: `-5/35 = -1/7`.
Now the expression is:
`-1/7 - 1/4`.
**Step 4: Find a common denominator**
The denominators are `7` and `4`. The least common denominator (LCD) is `28`.
Convert all terms:
`-1/7 = -4/28`
`-1/4 = -7/28`.
**Step 5: Combine the terms**
`-4/28 - 7/28 = (-4 - 7) / 28`
`= -11/28`.
**Final Answer for (ii):** `-11/28`.
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### Summary of Answers:
(i) `2`
(ii) `-11/28`