**Decimals (adding, subtracting, multiplying, and dividing)**

**Fractions (adding, subtracting, multiplying, and dividing)**

**Steps for Decimals Operation**

**Adding Decimals:**

**Align the decimal points of the two numbers.**

**Add the digits in each place value column.**

**If the sum of any column is 10 or more, carry over the extra digit to the next column.**

**Write the final sum with the decimal point in the same place as the original numbers.**

**Subtracting Decimals:**

**Align the decimal points of the two numbers.**

**Subtract the digits in each place value column.**

**If the digit in the minuend column is smaller than the digit in the corresponding subtrahend column, borrow from the next column to the left.**

**Write the final difference with the decimal point in the same place as the original numbers.**

**Multiplying Decimals:**

**Ignore the decimal points of the two numbers and multiply as if they were whole numbers.**

**Count the total number of digits to the right of the decimal point in the original numbers.**

**Place the decimal point in the product so that there are the same number of digits to the right of the decimal point as there were in the original numbers.**

**Dividing Decimals:**

**Move the decimal point in the divisor (the number being divided into the dividend) to the right until it becomes a whole number.**

**Move the decimal point in the dividend (the number being divided) to the right the same number of times as the divisor.**

**Divide the two numbers as we would with whole numbers.**

**Place the decimal point in the quotient directly above the decimal point in the dividend.**

**Question 1:**

**3.8 + 2.7 = ?**

**Solution: 6.5**

**Question 2:**

**8.9 – 3.2 = ?**

**Solution: 5.7**

**Question 3:**

**2.5 x 4.7 = ?**

**Solution: 11.75**

**Question 4:**

**9.6 ÷ 2.4 = ?**

**Solution: 4**

**Question 5:**

**7.4 + 5.2 – 2.9 = ?**

**Solution: 9.7**

**Question 6:**

**6.5 – 3.7 + 1.9 = ?**

**Solution: 4.7**

**Question 7:**

**1.2 x 0.5 = ?**

**Solution: 0.6**

**Question 8:**

**7.9 ÷ 1.3 = ?**

**Solution: 6.1**

**Question 9:**

**5.3 + 4.6 – 3.1 + 1.2 = ?**

**Solution: 8**

**Question 10:**

**6.7 – 3.2 + 2.1 – 0.9 = ?**

**Solution: 4.7**

**Question 11:**

**2.6 x 3.5 = ?**

**Solution: 9.1**

**Question 12:**

**8.4 ÷ 2.1 = ?**

**Solution: 4**

**Question 13:**

**3.7 + 1.8 – 0.9 + 2.4 – 1.3 = ?**

**Solution: 5.7**

**Question 14:**

**7.2 – 3.5 + 2.1 + 1.3 – 0.8 = ?**

**Solution: 6.3**

**Question 15:**

**4.5 x 1.2 = ?**

**Solution: 5.4**

**Question 16:**

**6.8 ÷ 2.4 = ?**

**Solution: 2.83**

**Question 17:**

**3.1 + 5.6 – 1.9 + 0.7 – 2.4 = ?**

**Solution: 4.1**

**Question 18:**

**5.2 – 2.7 + 1.8 + 2.1 – 0.9 = ?**

**Solution: 6.5**

**Fractions (adding, subtracting, multiplying, and dividing)**

**Fractions are a way of representing a part of a whole. They consist of two numbers, the numerator (top number) and the denominator (bottom number), separated by a horizontal line.**

**Adding and Subtracting Fractions**

**Question 1: **

**3/5 + 2/5**

**Step 1: Check to see if the denominators are the same. **

**In this case, they are both 5, so you can add the numerators.**

**Step 2: Add the numerators: 3 + 2 = 5**

**Step 3: Keep the denominator the same: 5**

**Step 4: Simplify, if possible: 5/5 = 1**

**Answer: 3/5 + 2/5 = 1**

**Question 2:**

**3/4 – 1/4**

**Step 1: Check to see if the denominators are the same. **

**In this case, they are both 4, so you can subtract the numerators.**

**Step 2: Subtract the numerators: 3 – 1 = 2**

**Step 3: Keep the denominator the same: 4**

**Step 4: Simplify, if possible: 2/4 = 1/2**

**Answer: 3/4 – 1/4 = 1/2**

**Requested by: Hameed**

**Question 3:**

**Find the sum of 3/8 and 5/6.**

**Solution:**

**Step 1: Find the least common multiple (LCM) of the denominators, which is 24.**

**Step 2: Convert the fractions to have a denominator of 24:**

**3/8 = (3 x 3)/(8 x 3) = 9/24**

**5/6 = (5 x 4)/(6 x 4) = 20/24**

**Step 3: Add the numerators: 9 + 20 = 29**

**Step 4: Write the sum as a fraction with the LCM denominator: 29/24**

**Answer: 29/24**

**Requested by: Hameed**

**Question 4:**

**Subtract 1/3 from 2/5.**

**Solution:**

**Step 1: Find the least common multiple (LCM) of the denominators, which is 15.**

**Step 2: Convert the fractions to have a denominator of 15:**

**1/3 = (1 x 5)/(3 x 5) = 5/15**

**2/5 = (2 x 3)/(5 x 3) = 6/15**

**Step 3: Subtract the numerators: 6 – 5 = 1**

**Step 4: Write the difference as a fraction with the LCM denominator: 1/15**

**Answer: 1/15**

**Requested by: Hameed**

**Question 5:**

**3/4 + 1/2 = ?**

**Solution:**

**Step 1: Find a common denominator: 4 x 2 = 8**

**Step 2: Convert both fractions to have a denominator of 8:**

**3/4 = 6/8**

**1/2 = 4/8**

**Step 3: Add the numerators: 6 + 4 = 10**

**Step 4: Keep the denominator the same: 8**

**Answer: 3/4 + 1/2 = 10/8**

**Requested by: Hameed**

**Question 6:**

**2/3 – 1/4 = ?**

**Solution:**

**Step 1: Find a common denominator: 3 x 4 = 12**

**Step 2: Convert both fractions to have a denominator of 12:**

**2/3 = 8/12**

**1/4 = 3/12**

**Step 3: Subtract the numerators: 8 – 3 = 5**

**Step 4: Keep the denominator the same: 12**

**Answer: 2/3 – 1/4 = 5/12**

**Requested by: Hameed**

**Question 7:**

**3/5 – 2/5 = ?**

**Solution:**

**Step 1: Check to see if the denominators are the same. In this case, they are both 5, so you can subtract the numerators.**

**Step 2: Subtract the numerators: 3 – 2 = 1**

**Step 3: Keep the denominator the same: 5**

**Answer: 3/5 – 2/5 = 1/5**

**Requested by: Hameed**

**Multiplying and Dividing Fractions**

**Question 1: **

**2/3 x 3/4**

**Step 1: Multiply the numerators: 2 x 3 = 6**

**Step 2: Multiply the denominators: 3 x 4 = 12**

**Step 3: Simplify, if possible: 6/12 = 1/2**

**Answer: 2/3 x 3/4 = 1/2**

**Requested by: Hameed**

**Question 2: **

**3/5 ÷ 1/2**

**Step 1: Invert the second fraction: 1/2 becomes 2/1**

**Step 2: Multiply the first fraction by the reciprocal of the second fraction: 3/5 x 2/1**

**Step 3: Multiply the numerators: 3 x 2 = 6**

**Step 4: Multiply the denominators: 5 x 1 = 5**

**Step 5: Simplify, if possible: 6/5**

**Answer: 3/5 ÷ 1/2 = 6/5**

**Requested by: Hameed**

**Question 3:**

**1/2 x 2/3 = ?**

**Solution:**

**Step 1: Multiply the numerators: 1 x 2 = 2**

**Step 2: Multiply the denominators: 2 x 3 = 6**

**Answer: 1/2 x 2/3 = 2/6**

**Requested by: Hameed**

**Question 4:**

**3/4 x 1/2 = ?**

**Solution:**

**Step 1: Multiply the numerators: 3 x 1 = 3**

**Step 2: Multiply the denominators: 4 x 2 = 8**

**Answer: 3/4 x 1/2 = 3/8**

**Requested by: Hameed**

**Question 5:**

**2/3 ÷ 1/4 = ?**

**Solution:**

**Step 1: Invert the second fraction: 1/4 becomes 4/1**

**Step 2: Multiply the first fraction by the reciprocal of the second fraction: 2/3 x 4/1**

**Step 3: Multiply the numerators: 2 x 4 = 8**

**Step 4: Multiply the denominators: 3 x 1 = 3**

**Answer: 2/3 ÷ 1/4 = 8/3**

**Requested by: Hameed**

**Question 6:**

**Multiply 2/3 by 5/4.**

**Solution:**

**Step 1: Multiply the numerators: 2 x 5 = 10**

**Step 2: Multiply the denominators: 3 x 4 = 12**

**Step 3: Write the product as a fraction: 10/12**

**Step 4: Simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:**

**10/2 = 5**

**12/2 = 6**

**Answer: 5/6**

**Requested by: Hameed**

**Question 7:**

**Divide 1/4 by 2/3.**

**Solution:**

**Step 1: Invert the second fraction (the divisor): **

**2/3 becomes 3/2.**

**Step 2: Multiply the fractions:**

**1/4 x 3/2 = (1 x 3)/(4 x 2) = 3/8**

**Step 3: Simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 1:**

**3/1 = 3**

**8/1 = 8**

**Answer: 3/8**

**Requested by: Hameed**

**Question 8:**

**Simplify 12/18.**

**Solution:**

**Step 1: Find the greatest common factor (GCF) of the numerator and denominator, which is 6.**

**Step 2: Divide both the numerator and denominator by 6:**

**12/6 = 2**

**18/6 = 3**

**Answer: 2/3**

**Requested by: Hameed**

**Question 9:**

**Multiply: 2/3 * 4/5**

**Solution:**

**To multiply fractions, we follow these steps:**

**Step 1: Multiply the numerators together.**

**Step 2: Multiply the denominators together.**

**Step 3: Simplify the resulting fraction, if possible.**

**Using these steps, we can solve the problem as follows:**

**Step 1: 2 * 4 = 8**

**Step 2: 3 * 5 = 15**

**Step 3: The resulting fraction is 8/15, which cannot be simplified further.**

**Therefore, 2/3 * 4/5 = 8/15.**

**Requested by: Hameed**

**Question 10:**

**Divide: 1/2 ÷ 2/3**

**Solution:**

**To divide fractions, we follow these steps:**

**Step 1: Flip the second fraction (the one after the division symbol) and turn the division symbol into a multiplication symbol.**

**Step 2: Multiply the first fraction by the flipped second fraction.**

**Step 3: Simplify the resulting fraction, if possible.**

**Using these steps, we can solve the problem as follows:**

**Step 1: 2/3 flipped becomes 3/2 and the division symbol becomes a multiplication symbol: 1/2 * 3/2**

**Step 2: 1 * 3 = 3 (numerator) and 2 * 2 = 4 (denominator): 3/4**

**Step 3: The resulting fraction cannot be simplified further.**

**Therefore, 1/2 ÷ 2/3 = 3/4.**

**Requested by: Hameed**

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