Fractions

Unlock the World of Math with Delicates Inn Learning Services!

Are you seeking fun, engaging, and effective ways to master math? Look no further! At Delicates Inn, we offer personalized learning plans, expert tutors, and interactive resources to make math simple and enjoyable for students of all ages. Start your math journey with us today and experience the difference!

These principles are fundamental in arithmetic and are widely used in various mathematical operations.

Basic Mathematical Principles

1. Sign Rules for Multiplication/Division

2. Finding Common Factors

Example: Common factors of 12 and 8

• Factors of 12: 1, 2, 3, 4, 6, 12
• Factors of 8: 1, 2, 4, 8
• Common factors: 2 and 4

3. Lowest Common Denominator (LCD)

Example: LCD of 6 and 4

1. Multiples of 6: 6, 12, 18, 24…
2. Multiples of 4: 4, 8, 12, 16…
3. Smallest common multiple: 12

4. Fraction Equivalence

¹⁄₂ = ^3×1⁄_3×2 = ³⁄₆

⁴⁄₁₀ = ^2×2⁄_2×5 = ²⁄₅

5. Converting Mixed Numbers

Example: 1²⁄₃

= ^{(1×3) + 2}⁄₃ = ⁵⁄₃

Let’s break down the content with examples for each principle:

1. Sign of answer when multiplying or dividing:
   • Multiplication:
     • +×+=++×+=+: 3×4=123×4=12
     • +×−=−+×−=−: 3×(−4)=−123×(−4)=−12
     • −×+=−−×+=−: −3×4=−12−3×4=−12
     • −×−=+−×−=+: −3×(−4)=12−3×(−4)=12
   • Division:
     • +÷+=++÷+=+: 12÷3=412÷3=4
     • +÷−=−+÷−=−: 12÷(−3)=−412÷(−3)=−4
     • −÷+=−−÷+=−: −12÷3=−4−12÷3=−4
     • −÷−=+−÷−=+: −12÷(−3)=4−12÷(−3)=4
2. Finding common factors:
   • Common factors of 12 and 8 are numbers that divide both 12 and 8 without leaving a remainder.
     • Factors of 12: 1, 2, 3, 4, 6, 12
     • Factors of 8: 1, 2, 4, 8
     • Common factors: 2 and 4
3. Finding the lowest common denominator (LCD) when adding and subtracting fractions:
   • To add or subtract fractions, they must have the same denominator. The LCD is the smallest number that both denominators divide into evenly.
     • For fractions with denominators 6 and 4:
       • Multiples of 6: 6, 12, 18, 24, …
       • Multiples of 4: 4, 8, 12, 16, 20, …
       • LCD is 12.
4. The value of a fraction is not changed if the top and bottom are multiplied or divided by the same number:
   • Multiplying numerator and denominator by the same number:
     • 12=3×13×2=3621​=3×23×1​=63​
   • Dividing numerator and denominator by the same number:
     • 410=2×22×5=25104​=2×52×2​=52​
5. Converting mixed numbers to fractions:
   • A mixed number consists of a whole number and a fraction. To convert it to an improper fraction:
     • Multiply the whole number by the denominator and add the numerator.
     • Example: 123=(1×3)+23=53132​=3(1×3)+2​=35​

Operations Order

Now, Let go deeper into Understanding Fraction Equivalence

Order of Operations (BIDMAS)

The order of operations is a set of rules that ensures everyone solves mathematical expressions the same way. The mnemonic BIDMAS helps you remember the correct order:

• B – Brackets
• I – Indices (powers and roots)
• DM – Division and Multiplication (left to right)
• AS – Addition and Subtraction (left to right)

Example 1: Sally and Rola’s Cakes

Sally and Rola are twins. Their friends give them identical cakes for their birthday. Sally eats 1/8 of her cake, and Rola eats 1/6 of her cake. How much cake is left?

Solution: Use BIDMAS to calculate the remaining cake for each twin and then add the results.

Example 2: Equipment Replacement Part

A part has broken on a machine and needs to be replaced. The replacement part must be between 8 1/7 cm and 6 1/7 cm long to fit. The diagram shows the replacement part. Will this part fit the machine? Explain your answer.

Solution: Compare the length of the replacement part with the given range using BIDMAS to simplify the fractions.