Question

$\frac{2}{3} \times ( - \frac{3}{7} ) - \frac{1}{6} \times \frac{3}{2} + \frac{1}{14} \times \frac{2}{5}$
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Answer 1

Answer:

-213/420

Step-by-step explanation:

-6/21 - 1/4 + 1/35

= (-120 - 105 + 12)/ 420

= -213/420

Answer 2

Question

$\sf \frac{2}{3}\times (\frac{-3}{7} ) - \frac{1}{6} \times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$

$\rule{300}{0.5}$

Answer

To solve this we need to apply BODMAS. BODMAS is an acronym for Brackets, Of, Division, Multiplication, Addition and Subtraction. So according to BODMAS we need to solve a problem in the order of Brackets then Of then Division then Multiplication then Addition and at last Subtraction.

Let's solve your question step-by-step

$\sf \frac{2}{3}\times (\frac{-3}{7} ) - \frac{1}{6} \times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$

Step 1: Do multiplication.

⇒ $\sf \frac{-6}{21} - \frac{3}{12}+\frac{2}{70}$

Step 2: Simplify all fractions.

⇒ $\sf \frac{-6 \div 3 }{21\div 3 } - \frac{3\div 3 }{12\div 3 }+\frac{2\div 2 }{70\div 2 }$

⇒ $\sf \frac{-2 }{7} - \frac{1}{4}+\frac{1 }{35 }$

Step 3: Do addition.

⇒ $\sf \frac{-2}{7}+\frac{1}{35}-\frac{1}{4}$

⇒ $\sf \frac{-2\times 5 }{7\times 5 }+\frac{1}{35}-\frac{1}{4}$

⇒ $\sf \frac{-10 }{35 }+\frac{1}{35}-\frac{1}{4}$

⇒ $\sf \frac{-9 }{35 }+-\frac{1}{4}$

Step 4: Do subtraction.

⇒ $\sf \frac{-9 }{35 }+-\frac{1}{4}$

⇒ $\sf \frac{-9 \times 4 }{35 \times 4 }+-\frac{1\times 35 }{4\times 35}$

⇒ $\sf \frac{-36}{140 }+-\frac{ 35 }{140}$

⇒ $\sf \frac{-71}{140}$

∴ $\bf \frac{2}{3}\times (\frac{-3}{7} ) - \frac{1}{6} \times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5} =\frac{-71}{140}$

$\rule{300}{0.5}$

Additional Information

What are rational number?

Rational numbers are numbers that can be represented in $\sf \frac{p}{q}$ form where p and q are integers and q≠0.

What are the properties of rational numbers?

Rational Numbers Properties are -

• Closure Property ⇒ Applies for Addition, Subtraction and Multiplication.
• Commutative Property ⇒ Applies for Addition and Multiplication.
• Associative Property ⇒ Applies for Addition and Multiplication.
• Distributive Property ⇒ a × (b + c) = (a × b) + (a × c)
• Additive Identity ⇒ 0
• Multiplicative Identity ⇒ 1

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