tobis,marcus,and dominic rode their bicycles to the arcade. tobis rode 12/5 miles, marcus rode 2 1/3 miles and dominic rode 9/4 miles. Which person rode closest to 2 miles?
one way is to convert all to decimals and compare.
the other way is to recall that for a given numerator, the larger the denominator, the smaller the value.
That is 1/10 is less than 1/7, and so on
Now, you have several numbers which are all greater than 2 by some amount Those amounts are
2/5, 1/3, and 1/4
We already know that 1/4 is less than 1/3.
2/5 = 6/15
1/3 = 5/15
so 1/3 is less than 2/5
so we see that 2 1/4 is the smallest of the three values. It exceeds 2 by the smallest amount.
To find out which person rode closest to 2 miles, we need to compare the distances each person rode to 2 miles.
First, we need to convert all the distances to a common fraction or decimal form. Let's convert them to fractions:
Tobis rode 12/5 miles.
Marcus rode 2 1/3 miles. We can convert this to a fraction by multiplying the whole number (2) by the denominator of the fraction (3), then adding the numerator (1). This gives us (2 * 3 + 1) / 3 = 7/3 miles.
Dominic rode 9/4 miles.
Now, let's find the differences between each person's distance and 2 miles:
For Tobis: 2 - 12/5 = (2 * 5 - 12) / 5 = 10/5 - 12/5 = -2/5 miles.
For Marcus: 7/3 - 2 = (7 - 2 * 3) / 3 = 7/3 - 6/3 = 1/3 mile.
For Dominic: 2 - 9/4 = (2 * 4 - 9) / 4 = 8/4 - 9/4 = -1/4 mile.
Comparing the absolute values of the differences, we can see that Tobis rode the closest to 2 miles. The absolute value of -2/5 is 2/5.
Therefore, Tobis rode closest to 2 miles.