Hello! My 10 year old daughter is having trouble understanding these preparation questions from her math teacher. I know the answer but I don't know how to explain it to her.. I'm sorry if that doesn't make any sense. When I was in 5th grade they taught us differently. Well anyway, on to the questions! (they are not graded btw)
Estimate the sums or differences of the fractions or mixed numbers:
1. 2 8/9 - 2 1/7
2. 8 12/31 + 4 5/6
3. 15 2/15 - 15 1/20
Thank you so much!!!!!!!!
~ Trisha
you are an answer mooching fraud. You were Mrs Johns five minutes ago. Get out of here.
Thats what people say when their afraid to ask question their self!
Hello Trisha! I'd be happy to help you explain these preparation questions to your daughter.
To estimate sums or differences of fractions or mixed numbers, we can use rounding and mental math. Here's how you can guide your daughter through each question:
1. 2 8/9 - 2 1/7:
- To estimate the difference, start by rounding each mixed number to the nearest whole number. In this case, 2 8/9 rounds to 3 and 2 1/7 rounds to 2.
- Now, subtract the rounded whole numbers: 3 - 2 = 1.
- Next, subtract the fractional parts: 8/9 - 1/7.
- To simplify, we need to find a common denominator for 9 and 7, which is 63. So, convert both fractions to have a denominator of 63.
- Multiply the numerator and denominator of 8/9 by 7: (8/9) * (7/7) = 56/63.
- Multiply the numerator and denominator of 1/7 by 9: (1/7) * (9/9) = 9/63.
- Now, subtract the converted fractions: 56/63 - 9/63 = 47/63.
- Finally, add the whole number difference from earlier: 1 + 47/63 = 1 47/63.
2. 8 12/31 + 4 5/6:
- To estimate the sum, round each mixed number to the nearest whole number. In this case, 8 12/31 rounds to 9 and 4 5/6 rounds to 5.
- Now, add the rounded whole numbers: 9 + 5 = 14.
- Next, add the fractional parts: 12/31 + 5/6.
- Again, find a common denominator for 31 and 6, which is 186. Convert both fractions to have a denominator of 186.
- Multiply the numerator and denominator of 12/31 by 6: (12/31) * (6/6) = 72/186.
- Multiply the numerator and denominator of 5/6 by 31: (5/6) * (31/31) = 155/186.
- Now, add the converted fractions: 72/186 + 155/186 = 227/186.
- Finally, add the whole number sum from earlier: 14 + 227/186 = 14 41/186.
3. 15 2/15 - 15 1/20:
- Similarly, round each mixed number to the nearest whole number. In this case, 15 2/15 rounds to 15 and 15 1/20 rounds to 15.
- Now, subtract the rounded whole numbers: 15 - 15 = 0.
- Next, subtract the fractional parts: 2/15 - 1/20.
- Find a common denominator for 15 and 20, which is 60. Convert both fractions to have a denominator of 60.
- Multiply the numerator and denominator of 2/15 by 4: (2/15) * (4/4) = 8/60.
- Multiply the numerator and denominator of 1/20 by 3: (1/20) * (3/3) = 3/60.
- Subtract the converted fractions: 8/60 - 3/60 = 5/60.
- Finally, add the whole number difference from earlier: 0 + 5/60 = 5/60.
I hope this helps! Remember to encourage your daughter to show her work and work through each step carefully. If she gets stuck at any point, she can always ask for further clarification or help. Good luck!