An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Compare fractions: 4 3 < 5 4 .
Compare numbers: 0.3 < 3 1 .
Increase £60 by 10% : £60 + 0.10 × £60 = £66 .
Decrease £40 by 10% : £40 − 0.10 × £40 = £36 .
Divide £56 in a 5 : 3 ratio: £35 : £21 .
Divide 28 in a 3 : 4 ratio: 12 : 16 .
Find full marks if 30 is 40% : x = 0.40 30 = 75 .
Sugar for 7 cakes: 5 150 × 7 = 210 g.
Calculate 5 4 − 2 1 = 10 3 .
Calculate 5 3 of 7: 5 3 × 7 = 5 21 .
5 4 , 3 1 , £66 , £36 , £35 : £21 , 12 : 16 , 75 , 210 g , 10 3 , 5 21
Explanation
Introduction Let's tackle these math problems one by one! We'll break down each question, showing all the steps clearly.
Comparing Fractions Question 1: We need to compare 4 3 and 5 4 . Converting these to decimals, we have 4 3 = 0.75 and 5 4 = 0.8 . Since 0.75"> 0.8 > 0.75 , we conclude that 5 4 is bigger.
Comparing Decimals and Fractions Question 2: We need to compare 0.3 and 3 1 . Converting 3 1 to a decimal, we get approximately 0.333 . Since 0.3"> 0.333 > 0.3 , we conclude that 3 1 is bigger.
Percentage Increase Question 3: We need to increase £60 by 10% . First, we calculate 10% of £60 : 0.10 × £60 = £6 . Then, we add this to the original amount: £60 + £6 = £66 .
Percentage Decrease Question 4: We need to decrease £40 by 10% . First, we calculate 10% of £40 : 0.10 × £40 = £4 . Then, we subtract this from the original amount: £40 − £4 = £36 .
Dividing in a Ratio Question 5: We need to divide £56 in the ratio 5 : 3 . The total ratio is 5 + 3 = 8 . One ratio unit is £56 ÷ 8 = £7 . So, the two parts are 5 × £7 = £35 and 3 × £7 = £21 .
Dividing in a Ratio Question 6: We need to divide 28 in the ratio 3 : 4 . The total ratio is 3 + 4 = 7 . One ratio unit is 28 ÷ 7 = 4 . So, the two parts are 3 × 4 = 12 and 4 × 4 = 16 .
Finding Full Marks Question 7: If 30 marks is 40% , we need to find the full marks. Let x be the full marks. We can set up the equation 0.40 x = 30 . Solving for x , we get x = 0.40 30 = 75 .
Scaling Quantities Question 8: If 150g of sugar is used for 5 cakes, we need to find how much is used for 7 cakes. The amount of sugar per cake is 5 150 = 30 g. So, for 7 cakes, we need 7 × 30 = 210 g of sugar.
Subtracting Fractions Question 9: We need to calculate 5 4 − 2 1 . To subtract these fractions, we need a common denominator, which is 10. So, 5 4 = 10 8 and 2 1 = 10 5 . Therefore, 5 4 − 2 1 = 10 8 − 10 5 = 10 3 .
Fraction of a Number Question 10: We need to calculate 5 3 of 7. This means we need to multiply 5 3 by 7: 5 3 × 7 = 5 21 = 4.2 .
Final Answers Here are the answers:
5 4
3 1
£66
£36
£35 and £21
12 and 16
75
210g
10 3
5 21 or 4.2
Examples
These types of math problems are used in everyday life. For example, when you are cooking and need to adjust the amount of ingredients based on a recipe, you use ratios and proportions. When you are shopping and there is a discount, you use percentages to calculate the new price. When you are splitting a bill with friends, you use ratios to divide the cost fairly. Understanding fractions is essential for measuring ingredients, calculating distances, and understanding time.
