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Home » How Much Is Half a 3/4 Cup? Discover the Instant Conversion You’ve Been Missing! - Abbey Badges

How Much Is Half a 3/4 Cup? Discover the Instant Conversion You’ve Been Missing! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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So we are looking for the smallest three-digit number $x$ such that $x...
Let $x = 60k$. Then we solve $60k \equiv 1 \pmod{7}$. Since $60 \equiv...
4k \equiv 1 \pmod{7}
Multiplying both sides by the modular inverse of 4 modulo 7, which is...
k \equiv 2 \pmod{7}
So $k = 7m + 2$. Then $x = 60k = 60(7m + 2) = 420m + 120$. We seek the...
x = 420m + 120 \geq 100 \Rightarrow m \geq 0
Try $m = 0$: $x = 120$ (valid, three-digit). Check $120 \mod 7 = 1$?
\div 7 = 17 \text{ remainder } 1 \Rightarrow \text{Yes}
Thus, the smallest such number is $\boxed{120}$.

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